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.

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,

Step 2

**Required conditions for the given function to apply mean value theorem:**

The given function is *f*(*x*) = 2*sec^{2}*x *on the interval [(–π/4), (π/4)].

- The function
*f*(*x*) = 2*sec^{2}*x*must be continuous on the interval [(–π/4), (π/4)]. - The function
*f*(*x*) = 2*sec^{2}*x*must be differentiable.

It is known that the function *f*(*x*) = 2*sec^{2}*x *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,

Step 3

**Find the value of f’(c):**

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

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