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Find the absolute max and min values of the function on the given interval and graph it:...

Question:

Find the absolute max and min values of the function on the given interval and graph it: {eq}g(x)=e^{-x^2} , -3\leq x\leq 1{/eq}

Absolute Maximum:

The maximum or minimum value of the function can be obtained by getting the critical points first that is by differentiating the function and then put it equal to 0

Answer and Explanation:

To find the absolute maximum and minimum we will differentiate the function:

{eq}g(x)=e^{-x^{2}} {/eq}

After differentiating we get:

{eq}g'(x)=-2xe^{-x^{2}}=0\\ x=0 {/eq}

Now let us check the value of the function at these points:

{eq}f(-3)=e^{-9}=1.23\times 10^{-4}\\ f(0)=1\\ f(1)=e^{-1}=0.36 {/eq}

The absolute maximum occurs at x=0

The absolute minimum occurs at x=1


Learn more about this topic:

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What is an Absolute Value?

from Math 101: College Algebra

Chapter 2 / Lesson 3
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