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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

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4.2.29
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
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4.2.29 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

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check_circleAnswer
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

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Step 2

Answer:

This function satifies mean value theorem

 

Step 3

(B)

We can use mean value theorem formu...

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Tagged in

Math

Calculus

Derivative

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