Question

Question #6e833

Answer 1

Solve the equation.

Explanation:

The conclusion of MVT says there is a `c` in `(1/2,2)` such that `f'(c) = (f(2)-f(1/2))/(2-(1/2))`

Find `f'(x) = 1+1/x^2` and `f(2)-f(1/2))/(2-(1/2)) = 2`.

The solutions to `1+1/x^2 = 2` are `-1` and `1`, but `c` is in `(1/2,2)`, so the only value for `c` is `1`.