Find the rate at which x changes with respect to t when dy/dt = 2, dz/dt = 20, x = 0, y > 0, and z = −3 for the equation: x + 2y^2 − z = 5

Answer 1

If x + 2y² - z = 5, x = 0, and z = -3, then 2y² must equal 2, so y = 1. We are told that y > 0, so it cannot be negative 1. We now have enough information to calculate dx/dt: Start by differentiating the equation with respect to t, getting dx/dt + 2y dy/dt - dz/dt = 0. Then substitute the known values of y, dy/dt, and dz/dt to obtain dx/dt + 4 - 20 = 0, or dx/dt = 16. Therefore, the answer to our problem is 16 units change in x per unit change in t.

Answer 2

x + 2y² - z = 5

Since x = 0 and z = 3, we have y² = 4. So, y = ±2. But y > 0. So, y = 2.

dx/dt + 4y(dy/dt) - dz/dt = 0

dx/dt + 8(2) - 20 = 0

dx/dt = 4