Question

Solve f´(2) if f(x) = x^3 – 6x^2 + 9x + 3

Answer 1

Step-by-step explanation:

f(x) = x³ − 6x² + 9x + 3

Take the derivative and evaluate at x = 2.

f'(x) = 3x² − 12x + 9

f'(2) = -3

Check for local minimums or maximums by setting f'(x) equal to 0.

0 = 3x² − 12x + 9

0 = x² − 4x + 3

0 = (x − 1) (x − 3)

x = 1 or 3

Evaluate f(x) at the critical values, and at the end points.

f(0) = 3

f(1) = 7

f(3) = 3

f(5) = 23

f(x) has a minimum of 3 and a maximum of 23.