Question
Asked Oct 29, 2019
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    1. Use a graph of  to estimate the maximum and minimum values. Then find the exact values.

    2. Estimate the value of  at which  increases most rapidly. Then find the exact value

44. f(x) x2e
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44. f(x) x2e

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Expert Answer

Step 1
  1. First, here we will use the graph of the function to estimate the maximum and minimum values.
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10 8 f(x) ze 2 (2,0.541) -2 10 8 (0,0) From graph it can be observed that the local maxima is 0.541 when x 2 and the local minima is 0 when x 0. It can be noticed that the local maximum is also the global minimum. 12

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Step 2

Now we find the exact v...

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f(x) x2e-* f'(x) 2xe*-x2e* f'(x) = 0 => 2xe xe-* = 0 хе * (2 — х) — 0 = Now For critical points = => 2 (Since ex is never equal to 0) => x = 0 or x So, the function is having the local maxima is 0.541 when x = 2 and the local minima is 0 when x = 0.

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Calculus

Derivative

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