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).