For the function f(x)=x−(4/x), find all values of c in the interval [4,6] that satisfy the conclusion of the Mean-Value Theorem. If appropriate, leave your answer in radical form. Enter all fractions in lowest terms.

c = ?

Question

For the function f(x)=x−(4/x), find all values of c in the interval [4,6] that satisfy the conclusion of the Mean-Value Theorem. If appropriate, leave your answer in radical form. Enter all fractions in lowest terms.

c = ?

anonymous · Answer

This is the Mean Value Theorem for differentiation, correct? If so, then it must satisfy this equation:

$$f'(c)= \frac{f(b)-f(a)}{b-a}.$$ Now, try plugging in a=4, b=6, and differentiate the function to get f'(x), which you can easily turn into f'(c). Now, solve for c.