What Happens When y is Very Large or Small in This Function?

[john3]

I am currently working on a project and I am stuck on the last question (g).
I will provide the questions and my work up until this point.
If anyone could help me, it would be greatly appreciated.
problems.

 

[Sudharaka]

Re: unsure of sketch

I am currently working on a project and I am stuck on the last question (g).
I will provide the questions and my work up until this point.
If anyone could help me, it would be greatly appreciated.
problems.

Hi john, :)

Welcome to Math Help Boards! :)

\[\frac{k}{j}\sqrt[3]{V}=\frac{2\pi-\frac{h}{r}}{\pi\frac{h}{r}-8}\sqrt[3]{\frac{\pi h}{r}}\]

So you have to sketch the graph between \(\frac{k}{j}\sqrt[3]{V}\) and \(\frac{h}{r}\). For this I suggest you use the First derivative test and the Second derivative test. Some useful videos that illustrates this procedure can be found >>here<< and >>here<<.

Kind Regards,
Sudharaka.

 

[Opalg]

Re: unsure of sketch

The hint suggests that you should write this function as $\displaystyle y=\frac{2\pi-x}{\pi x-8}\sqrt[3]{\pi x}$, and the question asks you to think about what happens when $y$ is either very large or very small. It may help to sketch the graph. But without even doing that, you can see that $y$ will be small if the numerator of the fraction is small, and $y$ will be large if the denominator of the fraction is small. From that, you should be able to say something about what the corresponding values of $x$ might be.