Question

What is the maximum number of relative extrema a polynomial function can have?

Answer 1

Relative extrema occur where the derivative is zero (at least for your polynomial function). So taking the derivative we get

20x3−3x2+6=0

This is a 3rd degree equation, now if we are working with complex numbers this equation is guaranteed to have 3 solutions by the fundamental theorem of algebra. But the number of real roots are 1 which can be found out by using Descartes' rule of signs. So the maximum number of relative extrema are 1.