Differentiaitng Problem (dy/dx)

[Cate]

Homework Statement

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!

 

[Dick]

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

 

[HallsofIvy]

Homework Statement

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

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

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


Thanks!

 

[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.

 

[HallsofIvy]

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

 

[Cate]

tangent line gets steeper?

 

[HallsofIvy]

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