The equation of the tangent at (2, 3) on the curve y2 = ax3 + b is y = 4x – 5. Find the values of a and b.
finding the slope of the tangent by differentiating the curve
m(tangent) at (2,3) = 2a
equation of tangent is given by y – y1 = m(tangent)(x – x1)
now comparing the slope of a tangent with the given equation
2a = 4
a = 2
now (2,3) lies on the curve, these points must satisfy
32 = 2 × 23 + b
b = – 7
8