The equation of the tangent at (2, 3) on the curve y 2 = ax 3 + b is y = 4x – 5. Find the values of a and b.

Question

Philoid · Accepted Answer

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