Mathxl homework 19

Question

Answer the following questions about the function whose derivative is

fprime ′​(x)equals=​x(x+2​).

a. What are the critical points of​ f?

b. On what intervals is f increasing or​ decreasing?

c. At what​ points, if​ any, does f assume local maximum and minimum​ values?

Answer 1

The critical points are 0 and -2.

f will be increasing for x>-1 and decreasing for x<-1

Local max at -2 and local min at 0

The best way to be sure about this is to graph f(x) using an arbitrary constant, f(x)=(x³/3)+x²+C