Question

For f(x)=|x^2-ax|
Find the maximum value of the function in the interval [a,0].

Answer 1

in this interval x(x-a)<0
so the function is
f(x)=|x^2-ax|=ax-x^2
f'(x)=a-2x
f'=0 ---> x=a/2
f(a/2)=a^2/2-a^2/4=a^2/4
f(0)=f(a)=0
so max of f(x) in this interval is a^2/4

Answer 2

thanks. can you please explain a little.
How did you get "in this interval x(x-a)<0"