Determine whether the Mean Value Theorem can be applied to f on the closed inter

Question

Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that

f '(c) =

.

If the Mean Value Theorem cannot be applied, explain why not.

f(x) = x1/2,    [0, 1]

Can the Mean Value Theorem be applied? (Select all that apply.)

Yes.No, f is not continuous on [a, b].No, f is not differentiable on (a, b).None of the above.

If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that

f '(c) =

. (Enter your answers as a comma-separated list. If the Mean Value Theorem cannot be applied, enter NA.)
c =  

Explanation / Answer

given f(x) = x1/2

yes  f is continuous on [0,1]. f is differentiable on (0,1)

f '(x)=(1/2)x-1/2

f '(x)=1/(2x1/2)

f '(c)=1/(2c1/2)

f '(c)=[f(1)-f(0)]/(1-0)

1/(2c1/2)=[(11/2)-(01/2)]/(1-0)

1/(2c1/2)=[1-0]/1

1/(2c1/2)=1

(2c1/2)=1

c1/2=1/2

c=(1/2)2

c=1/4

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