# Differentiaitng Problem (dy/dx)

1. Dec 20, 2007

### Cate

1. The problem statement, all variables and given/known data
Questions: Imagine a particle along the graph of the function y=x^2+2X. The X-component of the particle changes at a constant rate of 1cm /sec. First, evalute how fast the y-component of the particle is changing at the various points below. Then for each, explain why your answer makes sense with the shape of the graph in mind.

This is what I did:

Know:

dx/dt= 1

x= -3,-2,-1,1

Find:

dy/dt= ?

y=2X+2 dy/dt= 2(-3)+2 dx/dt =-4

and so on for all four values of x am I right?

Thanks!

2. Dec 20, 2007

### Dick

Um. I think so. y=x^2+2x. dy/dt=2x*dx/dt+2*dx/dt. Your notation is a little ambiguous.

3. Dec 21, 2007

### HallsofIvy

Staff Emeritus
You mean dy/dx= 2x+ 2 and then dy/dt= -4.

4. Dec 21, 2007

### Cate

Thanks guys, what about the seond half of the question? explain why your answer makes sense with the shape of the graph in mind.

5. Dec 21, 2007

### HallsofIvy

Staff Emeritus
Remember that the derivative is the slope of the tangent line. What happens to the tangent line to the graph as x gets larger?

6. Dec 21, 2007

### Cate

tangent line gets steeper?

7. Dec 21, 2007

### HallsofIvy

Staff Emeritus
Yes, and so how fast does y change compared with x?