Find the equation of the tangent and the normal to the curves at the i

1.	Find the equation of the tangent and the normal to the curves at the indicated points: y = x4 – 6x3 + 13x2 – 10x + 5 at (0, 5)
Answer» Given as y = x⁴ – 6x³ + 13x² – 10x + 5 at (0, 5) Differentiate with respect to x, to get the slope of tangent dy/dx = 4x³ - 18x² + 26x - 10 m(tangent) at (0,5) = -10 m(normal) at (0,5) = 1/10 The equation of tangent is given by y - y₁ = m(tangent)(x - x₁) y - 5 = -10x y + 10x = 5 The equation of normal is given by y - y₁ = m(normal)(x - x₁) y - 5 = (1/10)x

Find the equation of the tangent and the normal to the curves at the indicated points: y = x4 – 6x3 + 13x2 – 10x + 5 at (0, 5)

Answer»

Given as y = x⁴ – 6x³ + 13x² – 10x + 5 at (0, 5)

Differentiate with respect to x, to get the slope of tangent

dy/dx = 4x³ - 18x² + 26x - 10

m(tangent) at (0,5) = -10

m(normal) at (0,5) = 1/10

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

y - 5 = -10x

y + 10x = 5

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

y - 5 = (1/10)x