Question

Consider the function 1-7x^2 on the interval [-2, 7]. How do I find the average slope on this interval? Find the one point in which f'(c) is equal to the mean slope.

I assume this is the mean value theorem? I know that only because I tried to look how to do this up in my textbook. My teacher was absent today and this is due online, and I have absolutely no idea since we haven't gone over that concept. I managed to plug both 7 and 2 into f(x) and solve the mean slope function at -35, but how on earth do I find the point with that as the mean slope? My first thought was to get the derivative of the original function and instead of setting it to 0, set it to -35, but the answer I got isn't being accepted. :/ Not sure what to do at this point. Thanks for your help in advance!

Answer 1

Please see below.

Explanation:

You have already found that the average slope on the interval is `-35`.

Now you are asked to find the value of `x` where `f'(x) =`the average slope. Then give that value of `x` the name `c`.

Find `f'(x) = -14x`

Solve `f'(x) = -35` so solve `-14x = -35`

We find `x = 5/2`.

the `c` we seek is `c = 5/2`.

(Yes, this is related to the mean value theorem. It is the algebra problem of finding the `c` whose existence is asserted in the conclusion of MVT.)
(You should get used to using your textbook. That is not an unusual thing to expect students to do.)