# Determine the absolute extreme values, if any exist, of the function f(x) = 2^x \sin x on [-2,...

## Question:

Determine the absolute extreme values, if any exist, of the function {eq}f(x) = 2^x \sin x {/eq} on {eq}[-2, 6]. {/eq}

## Application of Derivative:

The absolute extreme values are the absolute maximum and absolute minimum values of the function over the interval {eq}[{a, b}] {/eq}. In the interval for the critical points, the largest value of the function is absolute maximum and the smallest value is the absolute minimum.

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We have,

{eq}f(x) = 2^x \sin x {/eq} on {eq}[-2, 6] {/eq}

Differentiating with respect to x by product rule we get,

{eq}f'(x) = (2^x)\sin(x) +...

Solving Min-Max Problems Using Derivatives

from

Chapter 15 / Lesson 1
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Max and min problems show up in our daily lives extremely often. In this lesson, we will look at how to use derivatives to find maxima and minima of functions, and in the process solve problems involving maxima and minima.