A point moves along the graph y= x^(5/2) so that its x coordinate increases at the constant rate of 2units/second. Find the rate at which its y coordinate is increasing as it passes the point (4 ,32)?

1 Answer
Aug 26, 2015

dy/dt = 40 (y-units)/second

Explanation:

If y= x^(5/2)

and dx/dt = 2 (x-units)/second.

find dy/dt when x=4 (and y=32).

Differentiate y= x^(5/2) with respect to t (use implicit differentiation):

dy/dt= 5/2x^(3/2) dx/dt

Substitue the known value for x and dx/dt and solve for dy/dt:

dy/dt= 5/2x^(3/2) dx/dt

= 5/2(4)^(3/2) (2)

= 40