Determine the maxcimum number of turning points of f fxx2x93

Determine the maxcimum number of turning points of f f(x)=-x2(x+9)3(x2-1)

Solution

f(x)=-x2(x+9)3(x2-1)

Any polynomial of degree n can have a minimum of zero turning points and a maximum of n1. However, this depends on the kind of turning point.

Sometimes, \"turning point\" is defined as \"local maximum or minimum only\". In this case:

here the degree of f(x) = 2+1+2=5

maximum number of turning points =5-1=4