Determine whether the Mean Value Theorem can be applied to f on the closed interval. If the Mean Value Theorem can be applied, find all values of c in the open interval (1/2,2) such that f'(c)= (f(b)-f(a))/(b-a).

f(x)=(x+1)/x [1/2,2]

I have found f'(c) from that formula, I just want to check my work and answer and need help to find what values of c are.

Question

Determine whether the Mean Value Theorem can be applied to f on the closed interval. If the Mean Value Theorem can be applied, find all values of c in the open interval (1/2,2) such that f'(c)= (f(b)-f(a))/(b-a).

f(x)=(x+1)/x  [1/2,2]

I have found f'(c) from that formula, I just want to check my work and answer and need help to find what values of c are.

angelwings996 · Answer

I believe a=1/2 and b=2. Am I correct on that?

steve816 · Answer

Looks like f is differentiable on all values in the closed interval. So yes, the mean value theorem can be applied.

steve816 · Answer

Yes your statement is correct.

angelwings996 · Answer

Okay so I got (3/2 - 3)/(2-1/2) which is (1/2)/(3/2) which if you simplify wouldn't it be f'(c) = 1/3? @steve816

angelwings996 · Answer

@AloneS

alones · Answer

Wait, $(3/2 - 3)/(2-1/2)$ is your question?

angelwings996 · Answer

No, that was what I got as the f'(c). I did the math of what f(b) is and f(a)

angelwings996 · Answer

I need to find the values of c. But i get f'(c) = 1/3 so I dont know if that is the answer or what or I need to plug 1/3 into the equation (x+1)/x