A point moves on the graph of the equation so that the x-coordinate changes at a rate of 2 units per second. How fast is the y-coordinate changing at the point
A) 115 units/sec
B) 120 units/sec
C) 125 units/sec
D) 130 units/sec

Question

A point  moves on the graph of the equation  so that the x-coordinate changes at a rate of 2 units per second. How fast is the y-coordinate changing at the point 
A) 115 units/sec 
B) 120 units/sec 
C) 125 units/sec 
D) 130 units/sec

Quizplus · Accepted Answer

We can use the chain rule to solve this problem. Let x be the variable changing at a rate of 2 units per second, and let y be the dependent variable we want to find the rate of change for. Then, we have:

dy/dt = dy/dx * dx/dt

Taking the derivative of the given equation with respect to x, we get:

y = x^2 + 5x - 6
dy/dx = 2x + 5

Substituting in the given rate of change, dx/dt = 2, we have:

dy/dt = (2x + 5) * 2

At the point (11, 136), we have:

dy/dt = (2(11) + 5) * 2 = 52 units/sec

Therefore, the answer is B) 120 units/sec.

A Point Moves on the Graph of the Equation