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

##### 1 Answer

Aug 18, 2016

At

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

Hence the function has a maximum at

#### Explanation:

#y=4x-x^2#

#dy/dx=4-2x#

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

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

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

At

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

Hence the function has a maximum at

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