Question

How do you find the maximum or minimum of `f(x)=-20x+5x^2+9`?

Answer 1

The function has a minimum at `x=2`

Explanation:

Given -

`y=-20x+5x^2+9`

`dy/dx=-20+10x`
`(d^2y)/(dx^2)=10> 0`

`dy/dx=0 => -20+10x=0`

`x=20/10=2`

At `x=2; dy/dx=0; (d^2y)/(dx^2)>0`

Hence the function has a minimum at `x=2`