Question

1. Find all points of inflection of the function f(x)=x^4+x^3
A. (0, 0) and (-½, -1/16)
B. (-½, -1/16)
C. (0, 0)
D. (0, 0) and (-¾, -27/256)
E. none of these
I got A. I found the second derivative and solved for x and plugged in the values to find the points.

2. Given that f(x)=-x^2+18x-78 has a relative maximum at x=9, choose the correct statement.
A. f’ is negative on the interval (negative infinity, 9)
B. f’ is negative on the interval (9, infinity)
C. f’ is positive on the interval (negative infinity, infinity)
D. f’ is positive on the interval (9, infinity)
E. none of these
I got B. I found the first derivative and critical number. I used the interval test and first derivative test to determine positive or negative.

3. Let f”(x)=4x^3-2x and let f(x) have critical values -1, 0, and 1. Determine which critical values give a relative maximum
A. -1
B. 0
C. 1
D. -1 and 1
E. none of these
I got A. I put the critical values into intervals and tested them to determine positive or negative

Thank you for checking my answers..

Answer 1

All 3 are correct