I am trying to solve a related rates problem. The problem states:
If y = 4x -x^3 and the x-coordinate is increasing at the rate of 1/3 unit/sec. How fast is the slope of the graph changing at the instant when x = 2?
I have done this:
Let dx/dt = 1/3 unit/sec
I derive the formula: dy/dt = 4 dx/dt - 3x^2 dx/dt
I substitute to solve for dy/dt.
dy/dt = 4(1/3) - 3(2^2)(1/3) = -8/3
and then I solve for the slope as (dy/dt)/(dx/dt) = (-8/3)/3 which is -8 unit/sec
But the answer is supposed to be -4 units/sec
What am I doing wrong?