Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x)=ln(x),[1,6] Yes, it does
Posted: Thu Jul 14, 2022 4:08 pm
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x)=ln(x),[1,6] Yes, it does not matter if f is continuous or differentiable, every function satisfies the Mean Value Theorem. Yes, f is continuous on [1,6] and differentiable on (1,6). No, f is not continuous on [1,6]. No, f is continuous on [1,6] but not differentiable on (1,6). There is not enough information to verify if this function satisfies the Mean Value Theorem. c=2.79
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x)=x1,[1,7] Yes, it does not matter if f is continuous or differentiable, every function satisfies the Mean Value Theorem. Yes, f is continuous on [1,7] and differentiable on (1,7). No, f is not continuous on [1,7]. No, f is continuous on [1,7] but not differentiable on (1,7). There is not enough information to verify if this function satisfies the Mean Value Theorem. c=3.0833
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x)=x1,[1,7] Yes, it does not matter if f is continuous or differentiable, every function satisfies the Mean Value Theorem. Yes, f is continuous on [1,7] and differentiable on (1,7). No, f is not continuous on [1,7]. No, f is continuous on [1,7] but not differentiable on (1,7). There is not enough information to verify if this function satisfies the Mean Value Theorem. c=3.0833