Question

What is the relative maximum and minimum of the function?

Answer 1

Take the derivitive
f'(x)=6x^2+2x-11

find where f'(x)=0
f'(x)=0 when x=-1.53089 or x=1.19756

we use a sign chart
test values to see where the signs are
(see attachment)
f'(-2)=(+)
f'(0)=(-)
f'(2)=(+)
max happens when sign changes from (+) to (-)
min happens when sign changes from (-) to (+)

according to the chart, max is at -1.53089 and min is at 1.19756

now evaluate the original function for x=-1.53089 and x=1.19756
f(-1.53089)=12.0078
f(1.19756)=-8.30405

max at (-1.53089,12) and min at (1.19756, -8.30405)
I may have rounded off differently, but


answer is 2nd option