Rate of change of the area of a rectangle…

"The height of a rectangle is 5 units more than the double of the base. Find the rate of change of the area when $$base =4$$."

Well, I tried to solve it, so I'll tell you what I've done, and you tell me if I've done it correctly.

First, I know that $$Area=base.height$$ and I also know that $$height=2b+5$$ So, if I replace it, I get $$Area=b.(2b+5)=2b^2 +5b$$

I want to find out $$dA/db$$, so the derivative of the Area is $$dA/db=4b+5$$, and if I replace the base with 4, I get $$dA/db=21$$ Is that the correct answer?

• Yeah. I think so. – Eval May 25 at 16:51
• Yes that's right. The only nit I have to pick is that you should write ${dA\over db}$ not ${dA\over dB}$ – saulspatz May 25 at 16:52

It is correct except one formality: You change the names of variables without notice. You changed $$Area$$ to $$A$$, then you changed $$base$$ to $$b$$ and then to $$B$$. It is a good habbit not to change the variable names without notice. In your short calculation, it's not so critical because I was able to easily understand it anyway. However, doing so (even once) in a larger work would make it very messy.