Determine the conditions on parameter such that the function will have critical points.
Critical points are defined as where or when does not exist. I was thinking it would be but the back of the book has the answer as being between and .
Was my reasoning correct or am I missing something? I'm not sure why has to be between and .
the derivative is correct.
note that critical values occur at x-values where the function is defined. is undefined when , so there are no values of where is defined and is undefined.
that leaves the critical values where
using the quadratic formula ...
for critical values to exist, the discriminant,
solve this inequality for