I keep getting stuck, any help is much appreciated!
Question:
A rectangle initially has the dimensions 2cm by 4cm. All sides begin increasing in length at a rate of 1cm/s. At what rate is the area of the rectangle increasing after 20 s.
The length will be $\displaystyle (4+t)$cm. The width will be $\displaystyle (2+t)$cm. What will the area be? Find something of the form $\displaystyle A=f(t)$ and differentiate this to get something of the form $\displaystyle \frac{dA}{dt}=f'(t)$.
Looks good. When $\displaystyle t=19$, the area is $\displaystyle (21)(23)=483$, and when $\displaystyle t=20$, the area is $\displaystyle (22)(24)=528$, an increase of $\displaystyle 45$, and when $\displaystyle t=21$, the area is $\displaystyle (23)(25)=575$, an increase of $\displaystyle 47$, which suggests that when $\displaystyle t=20$, the rate of increase is $\displaystyle 46$cm/s.