The gradient of a curve is given by dy/dx = 6sqrt(x) + 2. The curve passes through the point (16, 38). Find the equation of the curve.
dy/dx = 6x1/2 + 2 y = (62/3)x3/2 + 2x + c = 4x3/2 + 2x + c 38 = (4163/2) + (2*16) + c c = 38 - 256 - 32 = -250 y = 4x3/2 + 2x - 250
