A particle moves along the curve below. y = √ 8 + x 3 As it reaches the point ( 1 , 3 ) , the y -coordinate is increasing at a rate of 5 cm/s . How fast is the x -coordinate of the point changing at that instant? cm/s

The x-coordinate is changing at 10 cm/s

Step-by-step explanation:

Rate of Change

Suppose two variables x and y are related by a given function y=f(x). If they both change with respect to a third variable (time, for instance), the rate of change of them is computed as the derivative using the chain rule:

We have

Or, equivalently

We need to know the rate of change of x respect to t. We'll use implicit differentiation:

Solving for dx/dt

Plugging in the values x=1, y=3, dy/dt=5

The x-coordinate is changing at 10 cm/s