Question
Asked Mar 28, 2019
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Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval.

49. f(x) = 2 sec3x
-π π
4' 4
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49. f(x) = 2 sec3x -π π 4' 4

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Expert Answer

Step 1

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,

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Step 2

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)].

  • The function f(x) = 2*sec2x must be continuous on the interval [(–π/4), (π/4)].
  • The function f(x) = 2*sec2x must be differentiable.

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,

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Step 3

Find the value of f’(c):

The value of f’(c) is obtained from ...

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Tagged in

Math

Calculus