Question

1. Find all critical values for f(x)=(9-x^2)^⅗
A. 0
B. 3
C. -3,3
D. -3, 0, 3
E. none of these
I got D. I found the derivative and solved for critical numbers.

2. Find all intervals on which the graph of f(x)=(x-1)/(x+3) is concave upward
A. (negative infinity, infinity)
B. (negative infinity, -3)
C. (1, infinity)
D. (-3, infinity)
E. none of these
I got B. I found the first derivative. I found the second derivative. Then used the interval test to determine concavity.

3. Given f(x)=10-(16/x), find all c in the interval [2,8] that satisfies the Mean Value Theorem.
A. 4
B. 5
C. 8/5
D. + or - 4
E. none of these
I got A. I found f(2) and f(8) and used the MVT. I found the derivative of the function and plugged in c for x. I solved for c. And made sure answer was in the interval.

Thank you for checking my answers.

Answer 1

#1,2 are ok
#3:
f' = 16/x^2
16/x^2 = (8-2)/6 = 1
x^2=16
x=4 in [2,8]
So, (A) is correct