How would you solve this question: If at any point (x, y) on the curve, d 2y dx2 = 24x + 10, and if there is a horizontal tangent line at the point (0, 7), determine the equation of the curve.

Answer 1

This is a straight application of integration.

dy/dx = 12x² + 10x + C₁ ... since dy/dx = 0 when x=0, C₁ =0

y= 4x³ + 5x² + C₂

y passes through (0,7) which makes C₂ = 7.