Question

A point moves along the curve y=x^2+1 so that the x-coordinate increases at a constant rate of 5 units per second. When x=1, at what rate is the gradient of the curve increasing?

Thanks in advance to anyone who helps. Answer is 3

Answer 1

Sorry is meant to say:
A point moves along the curve y=x^3 so that the x-coordinate increases at a constant rate of 5 units per second. When x=1, at what rate is the gradient of the curve increasing?

Answer 2

dx/dt = 5
dy/dt = 3x^2 dx/dt

Now, the gradient is g(x) = dy/dx = 3x^2
the rate of change of the gradient is dg/dt = 6x dx/dt = 6*5 = 30

If the answer is supposed to be 3, then I must have misread the problem.
O course, there's always the chance that you mis-stated it ...