Question

Given: f(x) = x^3 - 4x
What are all values of c that satisfy the conclusion of the mean value theorem on the interval [-3,3]

Answer 1

First you want to find what the value of the function is at each of the boundaries:

f(-3)=-15
f(3)=15

The slope of the secant line can be determined with this information, which is 5. Now we need to find all the values of c such that the derivative function is equal to 5:

f'(c)=5=3c^2-4
9=3c^2c
c=\[+/-\sqrt{3}\]
We can check our answer by seeing what the slope is at c=+/-sqrt3:

f'(sqrt3)=3(sqrt3)^2-4
=3(3)-4
=5

The same is true for -sqrt3. Therefore the two c values that prove the mean value theorem is x=+/-sqrt3

Answer 2

so how did u get the slope 5?

Answer 3

oh wait, nvm c:

Answer 4

thank you <33

Answer 5

can you help me with another one please? :)

Answer 6

I determined slope by imagining a straight line that would go from (-3, -15) to (3, 15). If you take the change in y/change in x, you get 30/6, which is 5. But you got that already so good job =D

Answer 7

OHH, i thought you just divided 15 by 3

Answer 8

I can try, I was a little bit rusty with that mean value theorem problem, but I can try!