(This is a multipart question. I got the first part, which I will show, but I need help with part (b).)
Find and classify the critical points of f(x)=x?3??(2-x)?4?? as local maxima and local minima. Give the values of x in the order of increasing. Give exact answers (use fractions if necessary).
A critical point p of a function occurs when f?′??(p)=0 or when f?′??(p) in undefined. If f changes from decreasing to increasing at p then f has a local minimum point at p. If f changes from increasing to decreasing at p then f has a local maximum point at p.
(a) To start this problem, we need to find the first derivative of f(x)=x?3??(2-x)?4??. (I did this part, and got it correct.)
f?′??(x)=-4x?3??(2-x)?3??+3x?2??(2-x)?4?? OR f?′??(x)=x?2??(2-x)?3??(6-7x)
(b) Now solve this equation for x.
f?′??(x)=x?2??(2-x)?3??(6-7x)=0
x=
Give the values of x in the order of increasing.