  4.2.29Question HelpConsider the following function on the given interval [a,b]f(x)-4x on the interval ,8a. Determine whether the Mean Value Theorem applies to the given function on the interval [a,b]b. If so, find the point(s) that are guaranteed to exist by the Mean Value Theorem

Question help_outlineImage Transcriptionclose4.2.29 Question Help Consider the following function on the given interval [a,b] f(x)-4x on the interval ,8 a. Determine whether the Mean Value Theorem applies to the given function on the interval [a,b] b. If so, find the point(s) that are guaranteed to exist by the Mean Value Theorem fullscreen
Step 1

(A)

There are two conditions to check whether any function satisfies mean value theorem

(i)

That function needs to be continuous on given interval

Here, we know that x can not be only 0

and 0 does not lie on [1/8 , 8]

So, this function is continuous over entire interval

(ii)

Since, there is no sharpe edge in this function

and function is continuous on given interval

So, this function must be differentiable on (1/8 , 8)

So, this function satisfies mean value theorem

Step 2

This function satifies mean value theorem

Step 3

(B)

We can use mean value theorem formu...

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