Question

A particle moves along the curve y=7 x 2+4y=7 x 2+4 in such a way that its xx-coordinate is changing at a rate of −5−5 centimeters per second. At what rate is the particle's yy-coordinate changing when the particle is at the point where x=1x=1?

Answer 1

The y-coordinate is changing by the rate of -70 cm per sec.

Explanation:

Given equation,

`y = 7x^2 + 4`

Differentiating with respect to time (t),

`(dy)/(dt)=14x (dx)/(dt)`

We have,

`(dx)/(dt)=-5\text{ cm per sec}, x = 1`

`(dy)/(dt) = 14(1)(-5)=-70\text{ cm per sec}`