Question

Two variable quantities A and B are found to be related by the equation A^3 + B^3 = 9. What is the rate of change dA/dt at the moment when A=2 and dB/dt = 3?

Answer 1

3A^2 dA/dt + 3B^2 dB/dt = 0

If A=2, then 8+B^3=9, B=1

12 dA/dt + 9 = 0

dA/dt = -3/4