Does the function $f(x)=-8x +x^2$ have a maximum or minimum?

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Answer 1 · 2017-08-03T17:07:41

There is a minimum at $(4,-16)$

We need

$(x^n)'=nx^(n-1)$

Our function is

$f(x)=x^2-8x$

We calculate the first derivative,

$f'(x)=2x-8$

The critical point is when $f'(x)=0$

$2x-8=0$ , $=>$ , $x=4$

The second derivative is

$f''(x)=2$

As

$f''(x)>0$ , the function is convex at $x=4$

graph{x^2-8x [-31.13, 33.82, -22.35, 10.13]}

Does the function f(x)=-8x +x^2f(x)=-8x +x^2 have a maximum or minimum?