Suppose f is a differentiable function such that f′(x)≤2 for all x∈[1,3]. if f(1)=4, the mean value theorem says that f(3)≤v for what value of v? (choose v as small as possible.)

The mean value theorem is used to link the average rate of change and the derivative of a function.

The value of V is 8.

The given parameters are:

Mean value theorem states that:

If [a,b] and

(a,b),

Then there is a point c in (a,b), such that:  

From the question, we understand that: f is differentiable

This means that:

So, we have:

Substitute 4 for f(1)

Recall that:

The equation becomes

Cross multiply

Add 4 to both sides

From the question, we have:

By comparisons;

Hence, the value of V is 8.

Read more about mean value theorems at:

link

The MVT guarantees the existence of such that

Since for all , we have

so that .

its 60

4 x 12 = 48

3 x 4 = 12

48 + 12 = 60

yeeeet

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