Question

What is the relative maximum value of the function f(x) = -2x^3 + 3x^2 + 36x - 15.

Answer 1

A. f(x) has a relative maximum value at x = -2, and its value is f(-2) = -59.
B. f(x) has a relative maximum value at x = 3, and its value is f(3) = 66.
C. f(x) has a relative maximum value at x = -2, and its value is f(-2) = 66.
D. f(x) has a relative maximum value at x = 3, and its value is f(3) = -59.

Answer 2

take the derivative, set it equal to zero and solve for \(x\)

Answer 3

okay

Answer 4

so the derivative is -6x^2 + 6x + 36

Answer 5

after i set it to = 0 i get x = -2 and x = 3

Answer 6

what do i do next?

Answer 7

okay that was wrong
the first zero is a local min and the second is a local max
you can see it from the picture

Answer 8

ohh

Answer 9

local min is \(f(-2)=-59\) and local max is \(f(3)=66\)

Answer 10

ok

Answer 11

so its B

Answer 12

yes