Question

Does the mean value theorem apply for the function f(x) = tan(2πx) over the interval [0, 2]? Justify your answer.

Answer 1

Yes, the mean value theorem does apply for the function f(x) = tan(2πx) over the interval [0, 2].

Step-by-step explanation:

Yes, the mean value theorem does apply for the function f(x) = tan(2πx) over the interval [0, 2].

The mean value theorem states that if a function is continuous on a closed interval and differentiable on an open interval within that closed interval, then there exists at least one point in the open interval where the instantaneous rate of change (the derivative) of the function is equal to the average rate of change of the function over the closed interval.

In this case, the function f(x) = tan(2πx) is continuous and differentiable over the interval [0, 2], so the mean value theorem applies.