For the function, find all critical points or determine that no such points exist.
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.