# Find the absolute maximum and the absolute minimum for the function f(t) = 2 cos t + sin 2t in...

## Question:

Find the absolute maximum and the absolute minimum for the function f(t) = 2 cos t + sin 2t in the interval {eq}\left [ 0,\frac{\pi }{2} \right ]. {/eq}

## Absolute maximum and absolute minimum

It is the maximum and minimum value of the function at any absolute value. It is different from maxima and minima of a function there is only one absolute maximum and absolute minimum value of a function.

For this we have to find the critical points of function and then find value of the function at these critical points and the end point of the given interval.

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{eq}f(t)=2\cos t+\sin 2t\\ \text{Differentiating the above function with respect to t.}\\ f'(t)=-2\sin t+2\cos t\\ \text{For critical...

Solving Min-Max Problems Using Derivatives

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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.