The left-most x-intercept is at x = -6. The behavior of the graph near x = -6 is -8*(-6 + 1/2)^2*(x+6)^3 =

-8*(-11/2)^2*(x+6)^3 = -242 (x+6)^3.

What is the maximum number of turning points on the graph?

The maximum number of turning points on the graph is 4 (the degree of the polynomial (5) minus 1). However, in this case they are only 3 because x = - 6 has a multiplicity 2 as a root of the derivative f '.

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