Question 1: Find the value (or values) of c that satisfy the equation $\frac{f(b)-f(a)}{b-a}=f’(c)$ in the conclusion of the Mean Value Theorem for the given function on the given interval.

$$ f(x)=x^{\frac{5}{2}};\,[0,1] $$

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Question 2: Find the value (or values) of c that satisfy the equation $\frac{f(b)-f(a)}{b-a}=f’(c)$ in the conclusion of the Mean Value Theorem for the given function on the given interval.

$$ f(x)=2x+\frac{2}{x},\,\bigg[\frac{1}{18},18\bigg] $$

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Question 3: Find the value (or values) of c that satisfy the equation $\frac{f(b)-f(a)}{b-a}=f’(c)$ in the conclusion of the Mean Value Theorem for the given function on the given interval.

$$ f(x)=\sqrt{x-2},\,[2,8] $$

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Question 5: Find the value (or values) of c that satisfy the equation $\frac{f(b)-f(a)}{b-a}=f’(c)$ in the conclusion of the Mean Value Theorem for the given function on the given interval.

$$ f(x)=\ln(x-5), \, [6,12] $$

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Question 6: Find the value (or values) of c that satisfy the equation $\frac{f(b)-f(a)}{b-a}=f’(c)$ in the conclusion of the Mean Value Theorem for the given function on the given interval.

$$ f(x)=5x^3-7x^2,\,[-2,2] $$

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