"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?