Question

1. Given f(x)=-6/x, choose the correct statement
A. The graph of f is concave upward on the interval (negative infinity, 0)
B. The graph of f is concave downward on the interval (negative infinity, 0)
C. The graph of f is concave upward on the interval (negative infinity, infinity)
D. The graph of f is concave upward on the interval (0, infinity)
E. none of these
I got A. I found the first derivative. I found the second derivative. I used the interval test to determine concavity.

2. Which of the following statements is true of f(x)=-x^3+18x^2-105x+198
A. f is decreasing on the interval (6, infinity)
B. f is decreasing on the interval (5, 7)
C. f is decreasing on the interval (negative infinity, 5)
D. f is increasing on the interval (5, 7)
E. none of these
I got D. I found the first derivative and critical numbers. I used the interval test to determine increasing or decreasing.

3. Find all points of extrema on the interval [0,2pi] if y=x-cosx
A. (-1.-1+(3pi/2))
B. (pi, pi+1)
C. (-1, 0)
D. ((3pi/2), (3pi/2))
E. none of these
I got D. I found the derivative and when sinx=-1. I got that number and plugged it into the original function to find the point.

Thank you for checking my answers.

Answer 1

#1 ok
#2
f' = -3x^2+36x-105
= -3(x^2-12x+35)
= -3(x-5)(x-7)
f'>0 on (5,7), so D is correct

#3
y' = 1+sinx
y'=0 only at x = 3pi/2, so (D) is correct