Basic Calculus: Differentiation usage

[EEristavi]

Problem:
How fast is the area of a rectangle changing if one side is I0 cm
long and is increasing at a rate of 2 cm/s and the other side is 8 cm
long and is decreasing at a rate of 3 cm/s?I have 2 approach and I want to know which is correct, why and what am I missing

 

[BvU]

Hello EE,

Why do you use t=2 in the second approach ? Why not 1, 1/2, 1/10 or 1/1000 ? What is the limit for $t\downarrow 0$ ?

Oh, and read the PF rules -- they in fact don't allow me to answer your post as is...

 

[Ray Vickson]

Problem:
How fast is the area of a rectangle changing if one side is I0 cm
long and is increasing at a rate of 2 cm/s and the other side is 8 cm
long and is decreasing at a rate of 3 cm/s?I have 2 approach and I want to know which is correct, why and what am I missing

You should type out your solution; most helpers will not look at images of handwritten work. Read the thread "Guidelines for students and helpers", by Vela, for more on this issue.

 

[BvU]

Ray, I thought micromass posted the guidelines (link in post #2 -- and I see EE was indeed reading them Good!)

EE: In fact you worked out s alright in approach 2. $80 - 14 t - 6 t^2$. The derivative is correct too: ${dS\over dt} = 14 - 12 t$ and my

Why do you use t=2 in the second approach ?

was mistaken.
the rate of growth at $t=0$ comes out the same: $-14$ (but you forgot the minus sign in 1).

The rate of growth for other $t$ comes out the same too if you fill in the correct $b$ and $a$ !


And I agree with Ray about typing instead of posting a picture. But I ve seen a lot of pictures a lot worse than yours -- and this Is your first thread.

 

[Mark44]

But I ve seen a lot of pictures a lot worse than yours

I've seen a lot that were better, too. The image posted here is very small and not well lit, making it harder to read.

 

[EEristavi]

Thank you everyone for helping me and giving tips :)