Question

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = ln(x), [1, 9] Yes, it does not matter if f is continuous or differentiable, every function satisfies the Mean Value Theorem. Yes, f is continuous on [1, 9] and differentiable on (1, 9). No, f is not continuous on [1, 9]. No, f is continuous on [1, 9] but not differentiable on (1, 9). There is not enough information to verify if this function satisfies the Mean Value Theorem. 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). c =

Answer 1

Answer:

  Yes, f is continuous on [1, 9] and differentiable on (1, 9).

Step-by-step explanation:

The natural log function is continuous and differentiable on its domain of (0, ∞). So, it is continuous on any closed interval contained within this domain.

The function satisfies the hypotheses of the Mean Value Theorem on the interval [1, 9].