Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval.
Mean value theorem:
The statement of the mean value theorem says that, if a function f(x) is continuous and differentiable on the interval [a, b], then there exists a number c from the interval [a, b] that,
Required conditions for the given function to apply mean value theorem:
The given function is f(x) = 2*sec2x on the interval [(–π/4), (π/4)].
It is known that the function f(x) = 2*sec2x will be continuous and differentiable on the interval [(–π/4), (π/4)]. Therefore, the conditions of mean value theorem are true.
Thus, there exists a number c in the interval [(–π/4), (π/4)] with,
Find the value of f’(c):
The value of f’(c) is obtained from ...
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