1
$\begingroup$

"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?

$\endgroup$
  • 2
    $\begingroup$ Yeah. I think so. $\endgroup$ – Eval May 25 at 16:51
  • 2
    $\begingroup$ Yes that's right. The only nit I have to pick is that you should write ${dA\over db}$ not ${dA\over dB}$ $\endgroup$ – saulspatz May 25 at 16:52
0
$\begingroup$

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.

$\endgroup$

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.