What is the relative maximum value of the function f(x) = –x3 + 6x2 – 9x – 1?

–5
–1
1
3

-1.

Step-by-step explanation:

First find the derivative of f(x):

f'(x) = -3x^2 + 12x - 9 = 0   for a maximum or minimum.

-3(x^2 - 4x + 3) = 0

(x - 1)(x - 3) = 0

x = 1, 3.

To find which gives a relative maximum we find the second derivative:

f"(x) = -6x + 12

When x = 1  f"(x) = 6,    positive.

when x = 3, f"(x) = -6,  negative.

So x = 3 gives a maximum value of f(x).

f(3) = -(3)^3  + 6*(3)^2  - 9(3) - 1 = -1 (answer).