Question
Asked Nov 14, 2019
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f(x)= 2x^3+3x^2-36x

Determine whether the Mean Value Theorem can be applied to f on [-2,2]. If the mean value theorem can be applied, find all value(s) of c in the open interval (-2,2) that satisfies the theorem. 

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Expert Answer

Step 1

Given,

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f(x) 2x +3x2-36x, xe[-2,2]

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Step 2

Since f is a polynomial in x, so it is continuous in the interval [-2, 2] and differentiable in the interval (-2, 2).

Now

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d (x*)=r2e' n-1 f'(x)=2.3x2 +3.2x-36-1 = 6x2 +6x -36

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Step 3

Now by mean value theorem there ex...

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f(b)-f(a) f'(c)= b-а f(2)-(2) 2-(-2) — бс + бс —36 %— [2(2+3(2)-36(2)]-[2(-2)+3(-2) -36(-2)] 6c26c 36 = 4 6c26c 36 = 28 6c26c 64 0

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