For the polynomial function below a Determine the max number

For the polynomial function below: (a) Determine the max number of turning points on the graph. (b) find the power function that the graph of f resembles for the large values of |x|. (y= )

f(x)= -2(x-2)(x+6)²

Solution

f(x) = -2 (x-2)(x+6)^2

the maximum number of turning pointsof a nth degree polynomial is (n-1)

the degree of this polynomial is 3

therefore, maximum number of turning points would be (3-1 ) = 2

b) power function that the graph of f resembles for large values of x is

lim x -> infinity { -2 (x-2)(x+6)^2} = - x^3

therefore, function resembles y = - x^3