A point moves along the curve y=2x^2+1

[dnt]

A point moves along the curve y=2x^2+1 in such a way that the y value is decreasing at the rate of 2 units per second. At what rate is x changing when x=(3/2)?Ok here's what I've done...

Dy/dt=(4x)(dx/dt)

-2 = (4*3/2)(dx/dt)

So dx/dt=-1/3 (ie decreasing by 1/3 units per second)

First, is that right? Second when I look at the graph and y is decreasing it's the left side of the parabola however as I go down the graph the x increasing from left to right. So either my work is wrong above or I am misinterpreting the graph. What have I done wrong? Thanks.

 

[pasmith]

A point moves along the curve y=2x^2+1 in such a way that the y value is decreasing at the rate of 2 units per second. At what rate is x changing when x=(3/2)?Ok here's what I've done...

Dy/dt=(4x)(dx/dt)

-2 = (4*3/2)(dx/dt)

So dx/dt=-1/3 (ie decreasing by 1/3 units per second)

First, is that right?

Yes.

Second when I look at the graph and y is decreasing it's the left side of the parabola however as I go down the graph the x increasing from left to right. So either my work is wrong above or I am misinterpreting the graph. What have I done wrong? Thanks.

Looking at a graph of y against x only tells you how y varies with x. That graph tells you nothing about how y varies with t unless you know how x varies with t. If y increases with x but x itself is decreasing with t, then y will decrease with t.

 

[PeroK]

A point moves along the curve y=2x^2+1 in such a way that the y value is decreasing at the rate of 2 units per second. At what rate is x changing when x=(3/2)?Ok here's what I've done...

Dy/dt=(4x)(dx/dt)

-2 = (4*3/2)(dx/dt)

So dx/dt=-1/3 (ie decreasing by 1/3 units per second)

First, is that right? Second when I look at the graph and y is decreasing it's the left side of the parabola however as I go down the graph the x increasing from left to right. So either my work is wrong above or I am misinterpreting the graph. What have I done wrong? Thanks.

In which direction do you think the particle is moving? (You've not done anything wrong.)