Question

A particle moves along the curve below. y = 8 + x3 As it reaches the point (1, 3), the y-coordinate is increasing at a rate of 3 cm/s. How fast is the x-coordinate of the point changing at that instant?

Answer 1

Answer:

Change of rate of x coordinate=1 cm/s

Step-by-step explanation:

Given that

$y=8+x^3$

Now differentiate with respect to time in both side

So $\dfrac{dy}{dt}=0+3 x^2\dfrac{dx}{dt}$

Given  that y-coordinate is increasing at a rate of 3 cm/s

So $\dfrac{dy}{dt}=3$

Also given that coordinates (1,3)

So x=1

Now by putting the values

$3=0+3\times 1^2\dfrac{dx}{dt}$

So  $\dfrac{dx}{dt}=1$

Change of rate of x coordinate=1 cm/s