LECTURE 9
... changing with time. At a certain instant when x=1 and y=2, x is decreasing at the rate of 2 units/s, and y is increasing at the rate of 3 units/s. How fast is z changing at this instant? Is z ...
... changing with time. At a certain instant when x=1 and y=2, x is decreasing at the rate of 2 units/s, and y is increasing at the rate of 3 units/s. How fast is z changing at this instant? Is z ...
Homework 8 - UC Davis Mathematics
... 3. This problem is meant to give us some intuition about how derivatives and polynomials react to each other. (a) Compute f 00 (x) for f (x) = x + 1. (b) Compute f 000 (x) for f (x) = x2 + x + 1. d4 3 (x + x2 + x + 1). dx4 (d) Look at the number of derivatives you have taken and the powers on the fu ...
... 3. This problem is meant to give us some intuition about how derivatives and polynomials react to each other. (a) Compute f 00 (x) for f (x) = x + 1. (b) Compute f 000 (x) for f (x) = x2 + x + 1. d4 3 (x + x2 + x + 1). dx4 (d) Look at the number of derivatives you have taken and the powers on the fu ...
Basic concept of differential and integral calculus
... In the first case we can solve y and rewrite the relationship as In second case it does not seem easy to solve for Y. When it is easy to express the relation as y=f(x) we say that y is given as an explicit function of x, otherwise it is an implicit function of x ...
... In the first case we can solve y and rewrite the relationship as In second case it does not seem easy to solve for Y. When it is easy to express the relation as y=f(x) we say that y is given as an explicit function of x, otherwise it is an implicit function of x ...
Quant I Dist Assignment 2006
... c. Limit of all non continuous function does not exist. d. A function is said to be continuous if only the limit of the function exist. e. None of the above 2) A function f(x) is continuous at c if a. F(x) at c exist b. The limit of f(x) as x approaches to c exist and equals to f(c) c. If f is non d ...
... c. Limit of all non continuous function does not exist. d. A function is said to be continuous if only the limit of the function exist. e. None of the above 2) A function f(x) is continuous at c if a. F(x) at c exist b. The limit of f(x) as x approaches to c exist and equals to f(c) c. If f is non d ...
Chapter 4 Theory - AlexanderAcademics.com
... The second derivative is zero when x = ±1. It is never undefined since x2 + 3 ≥ 3 for all x. To determine concavity, do a sign chart (shown above at the right). From the chart you can tell that f is concave up on (-∞, -1) and (1, ∞) and concave down on (-1, 1.) The inflection points are (-1, 3/2) an ...
... The second derivative is zero when x = ±1. It is never undefined since x2 + 3 ≥ 3 for all x. To determine concavity, do a sign chart (shown above at the right). From the chart you can tell that f is concave up on (-∞, -1) and (1, ∞) and concave down on (-1, 1.) The inflection points are (-1, 3/2) an ...
Reading Assignment 5
... Analogous to single variable functions, relative extreme points can be found for functions of more than one variable. The first order conditions, FOC, state the first order partial derivatives are set equal and the resulting system of equations is solved. The FOC are a necessary, but not sufficient ...
... Analogous to single variable functions, relative extreme points can be found for functions of more than one variable. The first order conditions, FOC, state the first order partial derivatives are set equal and the resulting system of equations is solved. The FOC are a necessary, but not sufficient ...
Fundamental theorem of calculus part 2
... Increasing/decreasing functions and their derivatives ...
... Increasing/decreasing functions and their derivatives ...
Lesson 3-8: Derivatives of Inverse Functions, Part 1
... Let f x x5 3x 2 , and let f 1 denote the inverse of f . Given that 1, 2 is on the graph of f, find ...
... Let f x x5 3x 2 , and let f 1 denote the inverse of f . Given that 1, 2 is on the graph of f, find ...
The Fundamental Theorem of Calculus.
... The Fundamental Theorem of Calculus. The two main concepts of calculus are integration and differentiation. The Fundamental Theorem of Calculus (FTC) says that these two concepts are essentially inverse to one another. The fundamental theorem states that if F has a continuous derivative on an interv ...
... The Fundamental Theorem of Calculus. The two main concepts of calculus are integration and differentiation. The Fundamental Theorem of Calculus (FTC) says that these two concepts are essentially inverse to one another. The fundamental theorem states that if F has a continuous derivative on an interv ...
2.1: The Derivative and Tangent Line Problem
... Step 1: Let’s begin with an arbitrary point and call it c, f (c) . Then, let’s choose another point on the curve that has a horizontal distance of x away from our initial x value, c. We would call that new point c x, f (c x) . What is the slope of that secant line joining those two po ...
... Step 1: Let’s begin with an arbitrary point and call it c, f (c) . Then, let’s choose another point on the curve that has a horizontal distance of x away from our initial x value, c. We would call that new point c x, f (c x) . What is the slope of that secant line joining those two po ...
Derivative of secant
... Derivative of secant For example, let’s use our formula for taking the derivative of 1/v to take the derivative of the secant function. d d 1 d sec x = ...
... Derivative of secant For example, let’s use our formula for taking the derivative of 1/v to take the derivative of the secant function. d d 1 d sec x = ...
Mathematics 111, Spring Term 2010
... a) The concept of a function: input, process, output. b) Linear functions, slope, intercepts, equations of a line. c) Functional notation: the function f given by f (x) = (expression in x). d) Ways to represent functions, such as tables, graphs, expressions, and verbal descriptions. e) Graph transfo ...
... a) The concept of a function: input, process, output. b) Linear functions, slope, intercepts, equations of a line. c) Functional notation: the function f given by f (x) = (expression in x). d) Ways to represent functions, such as tables, graphs, expressions, and verbal descriptions. e) Graph transfo ...
Notes 2.1 and 2.2 – Linear Equations and Function Date:______
... A college purchased exercise equipment worth $12,000 for the new campus fitness center. The equipment has a useful life of 8 years. The salvage value at the end of 8 years is $2,000. Write a linear equation that describes the book value of the equipment each year. ...
... A college purchased exercise equipment worth $12,000 for the new campus fitness center. The equipment has a useful life of 8 years. The salvage value at the end of 8 years is $2,000. Write a linear equation that describes the book value of the equipment each year. ...
AP Calculus AB
... Steps for Solving Differential Equations: “Find a solution (or solve) the separable differentiable equation…” 1. Separate the variables 2. Integrate each side 3. Make sure to put C on side with independent variable (normally x) 4. Plug in initial condition and solve for C (if given) 5. Solve for the ...
... Steps for Solving Differential Equations: “Find a solution (or solve) the separable differentiable equation…” 1. Separate the variables 2. Integrate each side 3. Make sure to put C on side with independent variable (normally x) 4. Plug in initial condition and solve for C (if given) 5. Solve for the ...
15 - BrainMass
... A) Divide the coefficient by the old exponential value. B) Subtract the new exponential value from the coefficient. C) Multiply the coefficient by the new exponential value. D) Divide the coefficient by the new exponential value. ...
... A) Divide the coefficient by the old exponential value. B) Subtract the new exponential value from the coefficient. C) Multiply the coefficient by the new exponential value. D) Divide the coefficient by the new exponential value. ...
Section 2.2 - Basic Differentiation Rules and Rates of Change
... where it started after it has traveled. To calculate it in one dimension, simply subtract the final position from the initial position. In symbols, if s is a position function with respect to time t, the displacement on the time interval [a,b] is: ...
... where it started after it has traveled. To calculate it in one dimension, simply subtract the final position from the initial position. In symbols, if s is a position function with respect to time t, the displacement on the time interval [a,b] is: ...
Calculus BC Study Guide Name
... ___________ 52. Use of the Fundamental Theorem of Calculus to evaluate a definite integral ___________ 53. Mean Value Theorem for Integrals ___________ 54. Second Fundamental Theorem of Calculus ___________ 55. Integration by substitution (include change of limits for definite integrals) ___________ ...
... ___________ 52. Use of the Fundamental Theorem of Calculus to evaluate a definite integral ___________ 53. Mean Value Theorem for Integrals ___________ 54. Second Fundamental Theorem of Calculus ___________ 55. Integration by substitution (include change of limits for definite integrals) ___________ ...
A Summary of Differential Calculus
... 1. If f 0 is positive (negative) on an interval I, then f is increasing (decreasing) on I. This fact makes it possible to use f 0 to determine the values of x for which f has a relative maximum value or a relative minimum value. The first step is to find the critical points of f : points x in the d ...
... 1. If f 0 is positive (negative) on an interval I, then f is increasing (decreasing) on I. This fact makes it possible to use f 0 to determine the values of x for which f has a relative maximum value or a relative minimum value. The first step is to find the critical points of f : points x in the d ...
3.8 Derivatives of Inverse Trig Functions
... We could use the same techniques to find the derivatives of the other three inverse trigonometric functions: arccosine, arccotangent, and arccosecant, but it is much easier to think of the following identities. ...
... We could use the same techniques to find the derivatives of the other three inverse trigonometric functions: arccosine, arccotangent, and arccosecant, but it is much easier to think of the following identities. ...