Download Math 125 – Section 02

Math 125 – Section 03 – Calculus I
Take-Home Assignment 7 – John Tynan
Due Date: Wednesday November 7
Name:___________________________________
Score:______________
Show all work unless otherwise directed. If you use your calculator (for anything besides
arithmetic) to get the answer, explain what you did and why you did it. Point values for
each part are given in brackets. [22 total]
NO WORK = NO CREDIT!!
Answer the following TRUE/FALSE questions. Defend your answer, if it is true, explain
why, if it is false, give an example showing that it is false: [2 each]
1. A continuous function defined on a closed interval must attain a maximum value on
that interval.
2. It is possible for a function to have an infinite number of critical points.
3. A continuous function that increases for all x must be differentiable everywhere.
4. If f x   0 for all x in some interval I, then f is increasing on I.
5. If f c  0 then f has an inflection point at c, f c .
6. If f x   0 for all x in [a, b] then f attains its maximum value on [a, b] at b.
7. The graph of f x  
x2  x  6
has a vertical asymptote at x = 3.
x3
8. The graph of f x  
x2 1
has a horizontal asymptote of y  1 .
1 x2
9. The function f x   x  1 satisfies the hypotheses of the Mean Value Theorem on
the interval [0, 2].
10. If f c  0 and f c  0 then f c is neither a maximum nor minimum value.
11. If the graph of a differentiable function has three x-intercepts, then it must have at
least two points where the tangent line is horizontal.