Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 2x^3 - 3x^2 - 36x + 4, [-3, 4]
Step 1
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.
f '(x) = 6x^2 - 6x - 36
Step 2
We now solve f '(x) = 0 for x, which gives the following critical numbers. (Enter your answers as a comma-separated list.)
x = 3, -2
Step 3
We must now find the function values at the critical numbers we just found and at the endpoints of the interval [-3, 4].
f(-2) =
f(3) =
f(-3) =
f(4) =
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