Find the absolute maximum and absolute minimum values of f on the given interval

Question

Find the absolute maximum and absolute minimum values of f on the given interval.f(x) = 6x3 18x2 54x + 2,    

[2, 4]

Part 1 of 4

The absolute maximum and minimum values of f occur either at a critical point inside the interval or at an endpoint of the interval. Recall that a critical point is a point where f '(x) = 0 or is undefined. We begin by finding the derivative of f. 18x^2-36x-54

PART 2

We now solve

f '(x) = 0

for x, which gives the following critical numbers. (Enter your answers as a comma-separated list.)

Right answer please for part 2 and show me the work

Explanation / Answer

f'(x) = 0

18x^2-36x-54 = 0

x^2 - 2x -3 = 0

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

x = 3 and x = -1 are critical points.

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