Question

Does `f(x)=2x^2-8x+5` have a maximum or a minimum? If so, what is it?

Answer 1

`f(x)=2x^2-8x+5` has a minimum value of `(-3)` at `x=2`

Explanation:

A parabola with expressed in the form: `color(red)ax^2+bx=c`
has a maximum if `color(red)(a) < 0`
or a minimum if `color(red)(a) > 0`

`f(x)=color(red)2x^2-8x+5` must, therefore, have a minimum.

The minimum will occur when the tangent slope is `0`;
or expressed in another way, when the derivative of `f(x)` is equal to `0`

`(df(x))/(dx)=4x-8`

and `4x-8=0`
when `x=color(blue)2`

`f(x=color(blue)2) =2 * color(blue)2^2-8 * color(blue)2 + 5`
`color(white)("XX")=8-16+5`
`color(white)("XX")=-3`