Function with two equations [ f(x) = 4x + 1, x ≤ −1 & x^2 − 4, x > −1

Question

Consider the following function.
f(x) = 4x + 1,  x ≤ −1
          x^2 − 4, x > −1

Find the critical numbers of f.

Find the open intervals on which the function is increasing or decreasing. (using interval notation.)

Apply the First Derivative Test to identify the relative extremum. 

Answer 1

I will not answer this question for you, but I will tell you how to do it.

First, of all, graph the function (you may have to graph both parts and ignore the parts which are not relevan).

You will see immediately what the critical points are.

The function is continuous at x = -1 but it is not differentiable there.

If you still don't see the answer, please send me a message and I will try to help further.