Again, we need to use the quotient rule to find the derivative. Be careful when factoring out the negative signs.
Now we can investigate where f '(x) is undefined or zero. f '(x) is undefined when x = 0. However, this doesn't count as a critical point since x = 0 wasn't in the domain of f to begin with. f '(x) is zero when
-28(x + 1) = 0,
which is when
x = -1.
This is our only critical point.
If we look at a graph, we can see this critical point, but we need to zoom in a lot:
We need to be careful with the calculator. Make sure it's telling the correct answer.