A particle moves along the curve y=4x2+6 the x-coordinate is changing at a rate of 2 centimeters per second. What is the rate of y changing when the particle is at the point where x=5?

Question

The equation is 4x²+6

Answer 1

With our equation of y = 4*x^2 + 6 we first take it's derivative with respect to time.

dy/dt = 8*x*dx/dt

We are seeking "dy/dt" where "x" is given as 5 cm and "dx/dt" is given as 2 cm/s. Plugging these back into our derivative yields:

dy/dt = 8*(5)*(2)

dy/dt = 80 cm/s