How do you find the local extrema for #f(x) = 3x^5 - 10x^3 - 1# on the interval [-1,1]?
That function has no local extrema on that interval. (It does, of course, have global extrema on the closed interval.)
I take the definition of local maximum to be:
(For local minimum, reverse the inequality.)
Fermat's Theorem tells us that
Applying the first derivative test, we see that
If you are being graded based on your answer, check you grader's definitions of local extrema.
Some presentations of calculus may include clauses in the definition so that we need only an open interval,
In such a presentation, since we have restricted the domain of