How do you find the local max and min for #f(x)=2x^3 + 5x^2 - 4x - 3#?

1 Answer
Guillaume L.
May 11, 2018

#x=-2# is a local maximum, and #x=1/3# is a local minimum.
See explanations below.

Explanation:

#f(x)=2x³+5x²-4x-3#
What we know is that there's a local extremum when #f'(x)=0#
#f'(x)=6x²+10x-4#
#6x²+10x-4=0#
#6(x²+5/3x-2/3)=0#
#x²+5/3x-2/3=0#
#x²-x/3+2x-2/3=0#
#x(x-1/3)+2(x-1/3)=0#
#(x+2)(x-1/3)=0#
Now we can clearly see that when #x=-2# and #x=1/3#, #f'(x)=0#
Also, we know that out of roots, #f(x)=ax³+bx²+cx+d# take the sign of #-a# in #-oo# and the sign of #a# in #+oo#. Because of that, we can deduce that #x=-2# is a local maximum, and #x=1/3# is a local minimum.
\0/ here's our answer!

Related questions
See all questions in Classifying Critical Points and Extreme Values for a Function
Impact of this question
2521 views around the world
You can reuse this answer
Creative Commons License