Consider the following function and closed interval. f(x) = (x − 7)(x − 8)(x − 9), [7, 9]

Question

Consider the following function and closed interval.

f(x) = (x − 7)(x − 8)(x − 9),    [7, 9]

If f is differentiable on the open interval (7, 9), find f '(x).

 (If it is not differentiable on the open interval, enter DNE.)

f '(x) =

If Rolle's Theorem can be applied, find all values of c in the open interval (a, b)

 such that f '(c) = 0.

 (Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.)

c =  

Answer 1

Yes, the cubic polynomial is differentiable.

The easiest way to differentiate it is to multiply it out first.

Then set the derivative to 0 and solve...the derivative is a quadratic with big numbers but fairly easy to solve.

In my opinion it is instructive to graph the function to see what the solution means.