Question

1. Find all points of inflection of the function f(x)=x^4-6x^3
A. (0, 0)
B. (0, 0), (9/2, -2187/16)
C. (3, -81)
D. (0, 0), 3, -81)
E. none of these
I got D. I found the second derivative and solved for x and plugged values into original function to get points.

2. Find dy/dx for y=sec3x
A. 9sec3xtan3x
B. 3sec3xtan3x
C. 3sec^2(3x)
D. 3tan^2(3x)
E. none of these
I was unsure on this one. I got B. I found the first derivative...

Given that f(x)=-x^2+12x-34 has a relative maximum at x=6, choose the correct statement.
A. f’ is positive on the interval (6, infinity)
B. f’ is positive on the interval (negative infinity, infinity)
C. f’ is negative on the interval (6, infinity)
D. f’ is negative on the interval (negative infinity, 6)
E. none of these
I got C. I found the first derivative and critical number. I used the interval test and first derivative test to determine positive or negative.

Thank you for checking my answers.

Answer 1

all look good to me.

No reason to be unsure on #2. Just the chain rule.

If u = 3x,
y=sec u
y' = secu tanu u'