How do you find the local extrema for f(x)=5x-x^2?

1 Answer
Mar 8, 2016

I found x=5/2 and y=25/4 as coordinates of a point of maximum for our function.

Explanation:

We can derive our function (representing a Parabola) and set the derivative equal to zero: this will give us the x coordinate where the function neither increases nor decreases.
So:
f'(x)=5-2x
set equal to zero:
5-2x=0
and:
x=5/2
which corresponds to a y value of:
f(5/2)=5(5/2)-(5/2)^2=25/2-25/4=25/4

Graphically:
graph{5x-x^2 [-20.28, 20.28, -10.14, 10.14]}