Question

Can somebody help me with this problem: If y^3=25x^2, determine dx/dt when x=5 and dy/dt=-2

Answer 1

Implicit differentiation:

3y^2 dy/dt = 50x dx/dt


Now plug in........

Answer 2

3y^2(-2)=50(-5)dx/dt

Answer 3

We don't know 'y'

Answer 4

You are right...but you do know that x = 5, so substitute x = 5 into the original equation, and solve for y (that's part of the problem).

Answer 5

ah!

Answer 6

you get y^3 = 625
y = cube root of 625 or (625)^(1/3)

Answer 7

Now, you can easily finish to find dx/dt

Answer 8

Thanks for the help.

Answer 9

welcome.