Question

What is the relative maximum and minimum of the function?

Answer 1

Take the derivitive
f'(x)=3x^2+12x
find where it equals zero
it equal zero at x=0 and x=-4
find the y values
f(0)=-36
f(-4)=-4
the critical points are (0,-36) and (-4,-4)

make sign chart
evalutat f'(x) at x=-5 and x=-1 and x=1, and see their signs
f'(-5)=(+)
f'(-1)=(-)
f'(1)=(+)
see below attachment

max is where sign changes from (+) to (-)
min is where sign changes from (-) to (+)

so
max at (-4,-4)
min at (0,-36)
none of the options are correct, do you have te right problem?