Download AP Calculus BC – 3.6 Chain Rule 1

FST – Chapter 6: Root, Power, and
Logarithm Functions
6-1: nth Root Functions
6-2: Rational Power Functions
Goals: Evaluate b1/n and bm/n for b>0.
Describe properties of nth root functions and rational power
functions.
Use rational exponents to model situations.
Graph nth root functions and rational power functions.
Interpret graphs of nth root functions and rational power
functions.
nth root and nth root functions:



nth root: Let n be an integer with n ≥ 2. x is an
nth root of k if and only if xn = k.
Postulate (Power of a Power Property): For
any nonnegative base x and any nonzero real
exponents m and n, (xm)n = xmn.
nth root function: a function with equation y =
x1/n, where n is an integer greater than or equal
to 2.
Radical Notation:

radical notation: When x ≥ 0 and n is an integer
with n ≥ 2,
equals1nthe
n
xx
positive nth root of x.
When x < 0, and n is an odd integer with
n ≥ 3, n x equals the real nth root of x.
Rational Exponent Theorem:

Rational Exponent Theorem: For all positive
integers m and n, and all real numbers x ≥ 0,
the mth power of the
m
m
1
m
th root of x &
n

n
n
positive
n
x x   x

x
m
n

 
 x
 
m
1
n
 n xm
the positive nth root
of the mth power of x.
Postulates for Powers:
For any nonnegative bases x and y and nonzero
exponents, or any nonzero bases and integer
exponents:
mn
Product of Powers Property
x x  x
Power of a Product Property
xyn  x n y n
Quotient of Powers Property
xm
mn

x
, x  0
n
x
m
n
Power of a Quotient Property
n
x
xn
   n ,  y  0
y
 y
Exponent Theorems:

Zero Exponent Theorem: If x is any
nonzero real number, x0 = 1.

Negative Exponent Theorem: For all x >
0 and n a real number, or for all x ≠ 0
1
n
and n an integer,
x 
x
n
Rational Power Functions:


A rational power function is a function f
with equation of the form f(x) = xm/n,
where m and n are nonzero integers.
The domain and the range of rational
power functions are both the set of
nonnegative real numbers.
Assignments and Note:

CW: Lesson Masters 6-1 & 6-2.

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HW 6-1: #3, 4, 11, 12, 13, 16, 18.
HW 6-2: #2, 4, 6, 8, 10, 14, 15.

Chapter test next Friday.