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Blizzard [7]
3 years ago
13

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
Mathematics
1 answer:
Vedmedyk [2.9K]3 years ago
7 0

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

f'(c)=(f(b)-f(a))/(b-a)

First we must determine the endpoints:

f(49)=-119

f(4)=-4

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

f'(c)=3+2\sqrt{c}

Therefore:

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

Simplify:

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

c=81/4

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