Consider the function f(x)=−2x3+2x2−2x+2 find the average slope of this function on the interval (4,9). by the mean value theorem, we know there exists a c in the open interval (4,9) such that f′(c) is equal to this mean slope. find the value of c in the interval which works

Average slope =-242

c=6.67

Step-by-step explanation:

We are given that a function

and interval (4,9)

We have to find the average slope of the given function and value of c in the given interval.

Using mean value theorem

a=4 and b=9

f(9)=-1312

Substitute the values then we get

Hence, the average value of slope is -242.

We know that f'(c)=-242

Substitute x=c

Then

Dividing on both sides by 2

and

and c=-6 It is not possible because it does not lie in the given interval

Therefore,c=6.67 lie in the given interval