Find the equation of the tangent and the normal to the following curves at the indicated points:
y = x⁴ – 6x³ + 13x² – 10x + 5 at x = 1 y = 3

Question

Find the equation of the tangent and the normal to the following curves at the indicated points: y = x 4 – 6x 3 + 13x 2 – 10x + 5 at x = 1 y = 3

Philoid · Accepted Answer

finding slope of the tangent by differentiating the curve

m(tangent) at (x = 1) = 2

normal is perpendicular to tangent so, m₁m₂ = – 1

equation of tangent is given by y – y₁ = m(tangent)(x – x₁)

y – 3 = 2(x – 1)

y = 2x + 1

equation of normal is given by y – y₁ = m(normal)(x – x₁)

Find the equation of the tangent and the normal to the following curves at the indicated points:y = x4 – 6x3 + 13x2 – 10x + 5 at x = 1 y = 3