Module calculus problem

Question

Given the relationship 2x² + y³ =10, with y > 0 and  = 3 units/min., find the value of  at the instant x = 1 unit.

Options:

1. -9 units/min
2. - units/min
3. -13/2 units/min
4. -1/9 units.min

Answer 1

Assuming that both x and y are functions of t, you should start by taking the derivative of your original expression with respect to t.

d/dt [ 2x² + y³ = 10]

This yields

4x (dx/dt) + 3y² (dy/dt) = 0

Now you can plug in all of the known values of the problem. First off, x = 1 and dy/dt = 3. Further, you can solve for y when x = 1 using your original expression and find that when x = 1 y can only take the value 2. Plug all of these values into the expression that relates the derivatives of x and y and you should arrive at the final answer.