Question
Asked Oct 9, 2019
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Find the absolute extrema of the function on the closed interval. Use a graphing utility to verify your results. (If an answer does not exist, enter DNE.)

f(x) = x3 − 27x,    [0, 6]
absolute maximum     (x, y)  = 
 
 
 
 
 
 
 
absolute minimum     (x, y)  = 
 
 
 
 
 
 
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Expert Answer

Step 1

Given a function 

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f(x) %3 х3 — 27х,

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Step 2

To find: Absolute extrema of a function in closed interval [0, 6].

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First, we begin with finding the critical points ie.f'(x)0 3x2 27 0 3x2 27 x29 - x =+3

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Step 3

Now, substitute the point...

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f(3) 33 27 3 = -54 f(-3) 33 27* -3 54 The absolute maxima don't exist as x -3 is outside the given interval [0, 6] The absolute minimum exists at x 3

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Tagged in

Math

Calculus

Derivative