Question

What value(s) of x is guarenteed by the Mean Value Theorem for...

Answer 1

\[f(x)=2x^3+x^2\]

Answer 2

I did MVT and got 15

Answer 3

But when I tried to plug it back in to the prime of the original equation I got confused

Answer 4

and set it to 15 btw

Answer 5

The MVT states that if f(x) is continuous and on the interval [a,b] and differentiable on (a,b) than there is at least one point c such that (a<c<b).

So, basically you are just finding the critical points of f(x)
What is f'(x)?
When is f'(x) = 0 / Undefined?

Answer 6

is there some interval given?

Answer 7

[-3,0] is the interval

Answer 8

Find the derivative of f(x). What value of c is guaranteed according to the MVT on interval (a,b) after differentiating... in this case the interval is [-3,0]. Hope I helped!

Answer 9

okay so so far i've done f(b)-f(a)/b-a

Answer 10

i got 15

Answer 11

What the MVT says is basically if you connect the endpoints with a secant lline, there is some point in between there where the tangent to the graph has the same slope as that line connecting the endpoints.