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

Answer:

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

Step-by-step explanation:

Given equation,

$y = 7x^2 + 4$

Differentiating with respect to time (t),

$\frac{dy}{dt}=14x \frac{dx}{dt}$

We have,

$\frac{dx}{dt}=-5\text{ cm per sec}, x = 1$

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