Question

The average cost function associated with producing and marketing x units of an item is given by AC$=2x-11+\frac{50}{x}$. Find the range of values of the output x, for which AC is increasing.

Answer 1

Now to find $AC$ increasing, we will differentiate the function of average cost and see at critical points.

$\frac{d\left(AC\right)}{dx}=2-\frac{50}{x^2}=0\Rightarrow x=-5,5$

Now if we plot it on number line we can see that functions value increases from $(-\infty ,-5),(5,\infty )$ and decreases from $(-5,5)$.

Hence range of values of the output $x$, for which $AC$ is increasing is $(-\infty ,-5)\cup (5,\infty )$