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Determine if the function f(x) = 4√x − 3x satisfies the Mean Value Theorem on [4, 49]. If so, find all numbers c on the interval that satisfy the theorem.
a) c = 812b) c = −814c) c = 818d) c = 814

Respuesta :

Answer:

c

Step-by-step explanation:

The mean value theorem states that for a continuous and differentiable function on a interval there exists a number c from that interval, that

[tex]f'(c)=(f(b)-f(a))/(b-a)[/tex]

First we must determine the endpoints:

[tex]f(49)=-119[/tex]

[tex]f(4)=-4[/tex]

We find the derivative of the function, f'(c)

[tex]f'(c)=3+2\sqrt{c}[/tex]

Therefore:

[tex]3+2\sqrt{c}=((-119)-(-4))/((49)-(4))[/tex]

Simplify:

[tex]3+2\sqrt{c}=-23/9[/tex]

[tex]c=81/4[/tex]

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