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Find the absolute maximum and absolute minimum value of the function f (t) = t - cube root of t...

Question:

Find the absolute maximum and absolute minimum value of the function {eq}f (t) = t - \sqrt[3] t {/eq} on the interval {eq}[-2,\ 1] {/eq}.

Extrema

Extrema are the values where a function reaches a maximum or a minimum. Local extrema must be critical points if the function is differentiable. Critical points are points where the derivative is 0.

Answer and Explanation:

First, let's find the derivative.

{eq}f'(t) = 1 - \frac{1}{3}t^{-2/3} {/eq}

Secondly, let's find the critical points:

{eq}f'(t) = 1 -...

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