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Find and classify the critical points of f

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(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.

Reference no: EM132078175

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