Continues (- infinity , infinity) find c
[ cx^2 + 8x
if x < 5
X^3 - cx if x> 5

It sounds like you're asked to find c such that f(x), defined by

is continuous at x = 5.

With the strict inequalities given in the definition, this is not possible. So you probably meant to use ≤ or ≥ in one of the pieces of the definition.

In order for f(x) to be continuous at x = 5, the limit from either side as x approaches 5 must be the same.

We have

and

Then

  the correct choice is marked

step-by-step explanation:

the first two graphs show multiple turning points. the last graphs matches the description in every detail.