precalculus
posted by Melinda on .
Determine the maximum and minimum number of turning points for the function h(x) = 2x^4  8x^3 + 5x 6.
Maximum:3
Minimum:1
Is this a valid reason:
A quartic polynomial function has a 3 Turning points. The turning point is always 1 less than the degree. For example degree 4=3 TP, degree 5=4 turning points?
What about the minimum?

A polynomial of odd degree n has at most n1 turning points, and may have none.
Think of a line or the curve for y=x^3.
A polynomial of even degree n may have at most n1 turning points, but must have at least one. Think of a parabola or y=x^4. An evendegree polynomial opens up or down, but must have a min or max.