Question

What is the relative maximum and minimum of the function?

f(x)= 2x^3 + x^2 – 11x


The relative maximum is at (–1.53, 8.3) and the relative minimum is at (1.2, –12.01).

The relative maximum is at (–1.53, 12.01) and the relative minimum is at (1.2, –8.3).

The relative maximum is at (–1.2, 8.3) and the relative minimum is at (1.53, –12.01).

The relative maximum is at (–1.2, 12.01) and the relative minimum is at (1.53, –8.3).

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