Question

Find all numbers c that satisfy the mean value theorem

Answer 1

We have that:

f(0)=−7

f(2)=83

f′(x)=27x2+9

Then, there exists a cin (0,2)

such that:

f′(c)=f(2)−f(0)2−0=83+72=45

This means that you have to solve the following:

f′(c)=45⇒27c2+9=45⇒3c2−4=0

Solutions are c=±23√3=±1.1547…

Only c=23√3

is inside the set (0,2)

Answer 2

,that is answer....................