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

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Answer 1 · 2016-12-06T12:30:10

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

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 $x=color(blue)2$

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

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