How to find the global equation of a dual curve?

How to find the equation and the set of values for the curve? PLEASE HELP, 10 POINTS?

• A curve is such that dy/dx = 3 / (1+2x)^2 and the point (1, 1/2) lies on the curve. Find the equation of the curve. Then find the set of values of x for which the gradient of the curve is less than 1/3. Please help, 10 points?

• Answer:

  dy = 3 dx / (1+2x)^2 Let u = 1 + 2x, then (1/2) du = dx dy = (3/2) du / u^2 y = -(3/2) (1/u) + C y = - 3 / (2+4x) + C Since (1,1/2) lies on the curve, we have 1/2 = (-3/6) + C so if my algebra is right, C has to be 1. The curve is: y = 1 - [ 3/(2+4x) ] I guess the next part is asking when dy/dx < 1/3. Looks like |x| needs to be greater than 1, which makes the denominator of dy/dx greater than 9.