Question

How do you find the max or minimum of `f(x)=-4x^2+5x`?

Answer 1

`"maximum value "=25/16`

Explanation:

`"using the method of "color(blue)"completing the square"`

`• " ensure coefficient of "x^2" term is 1"`

`• " add/subtract "(1/2"coefficient of x-term")^2`

`f(x)=-4(x^2-5/4x)`

`color(white)(f(x))=-4(x^2-2(5/8)xcolor(red)(+25/64)color(red)(-25/64))`

`color(white)(f(x))=-4(x-5/8)^2+25/16`

`(x-5/8)^2>=0" for "x inRR`

`rArr"maximum value "=25/16" when "x=5/8`
graph{-4x^2+5x [-10, 10, -5, 5]}