0
$\begingroup$

I was reading a document , where I stucked in figuring out this equation.

$f(k)= k^2-nk+\frac{n^2 - n}{2}$. This is a quadratic function of $k$. It is minimized when $k=\frac{n}{2}$ (the $k$ coordinate of the vertex of the parabola that is the graph of this function) and maximized at the endpoints of the domain, namely $k=1$ and $k=n-1$.

please explain how it is ??

$\endgroup$
  • $\begingroup$ What is your question exactly? Also, a quadratic equation has domain $\mathbb{R}$. $\endgroup$ – rae306 Sep 16 '14 at 18:18
  • 1
    $\begingroup$ What does your question have to do with differential equations, the (only) tag you used. Isn't this just a precalculus question? $\endgroup$ – Dave L. Renfro Sep 16 '14 at 18:18
  • $\begingroup$ As asked earlier,exactly what is the domain for $k$? $\endgroup$ – Macavity Sep 16 '14 at 18:26
2
$\begingroup$

Hint: $$f(k) = \left(k-\frac{n}2\right)^2+\frac{n^2-2n}4$$ So as the distance of $k$ from $\dfrac{n}2$ increases, the function increases.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.