Question:

A curve is such that dy/dx = 2x² − 5. Given that the point (3, 8) lies on the curve, find the equation of the curve.

Attempt:

dy/dx = 2x²-5

x = 3

2(3)²-5 = 13

y - y1 = m (x - x1)

y - 8 = 13 (x - 3)

y - 8 = 13x - 39

y = 13x - 39 +8

y = 13x -31