Question

Arrange the polynomial equations in increasing order of the maximum number of extrema they could have. y = x6 − 6x3 + 5x y = x5 + 4x3 − 5x y = x3 + 21x2 + 110 y = 3x2 + 5 y = x4 − 17x2 + 72 ↓ ↓ ↓ ↓

Answer 1

The increasing order of maximum number of extrema they could have is;

• y = 3x² + 5
• y = x³ + 21x + 2
• y = x⁴ − 17x² + 72
• y = x5 + 4x³ − 5x
• y = x6 − 6x3 + 5x

What is the maximum number of extrema they could have in increasing order?

The extrema of a polynomial is otherwise termed it's "turning point(s)". It follows that a polynomial with a degree n would have (n-1) number of turning points. It therefore follows on this basis that the arrangement of the polynomial equations in increasing order of possible extrema they could have is;

y = 3x² + 5

y = x³ + 21x + 2

y = x⁴ − 17x² + 72

y = x5 + 4x³ − 5x

y = x6 − 6x3 + 5x

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