How do you find the local maximum and minimum values of #f(x) = 2x^3 - 5x +1# in the the interval is (-3,3)?

1 Answer
Nov 15, 2016

#x=-sqrt(5/6)# is a local maximum
#x=sqrt(5/6)# is a local minimum
graph{2x^3-5x+1 [-10, 10, -5, 5]}

Explanation:

Find local extrema on the interval by finding where #f'(x)# is equal to zero. First find #f'(x)#

#f(x)=2x^3-5x+1#

#f'(x)=6x^2-5#
#0=6x^2-5#
#5=6x^2#
#x^2=5/6#
#x=+-sqrt(5/6)#
#xapprox+-.9129#

Find whether each is a local max or local min by checking values around #+-sqrt(5/6)#;
#x=-sqrt(5/6)# is a local maximum
#x=sqrt(5/6)# is a local minimum