Question

If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the mean value theorem. (enter your answers as a comma-separated list. if it does not satisfy the hypotheses, enter dne). lnx

Answer 1

Yes, f is continuous on [1,7] and differentiable of (1,7).f(x) - in x, [1,7], f is continuous and differentiable on (0, ∞ ), so f is continuous on [1, 7] and differentiable on (1, 7 ). f'(c) = (f(b) - f(a) / b - a) = 1/c = f(7) - f (1) / 7-1 = In 7/6 = c = 6/In 7, which is in (1,7). C is equal to 6 / In 7 which is also in (1,7)