How do you find the exact relative maximum and minimum of the polynomial function of #f(x)=4x-x^2#?

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Answer 1 · 2016-08-18T05:41:16

At #x=2#

#dy/dx=0# and #(d^2y)/(dx^2)<0#

Hence the function has a maximum at #x=2#

#y=4x-x^2#

#dy/dx=4-2x#

#dy/dx=>4-2x=0#

#x=(-4)/(-2)=2#

#(d^2y)/(dx^2)=-2#

At #x=2#

#dy/dx=0# and #(d^2y)/(dx^2)<0#

Hence the function has a maximum at #x=2#

graph{4x-x^2 [-10, 10, -5, 5]}