precalculus

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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?

  • precalculus -

    A polynomial of odd degree n has at most n-1 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 n-1 turning points, but must have at least one. Think of a parabola or y=x^4. An even-degree polynomial opens up or down, but must have a min or max.

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