Question

Find the equations of the tangent and the normal to the given curve at the indicated point for y = x⁴ - 6x³+13x² - 10x+5 at the point where x = 1

Answer 1

m : dy/dx = 4x³ - 18x²+26x - 10

m at (x = 1) = 2

y at (x = 1) = (1)⁴ – 6(1)³ + 13(1)² – 10(1) + 5 = 3

Tangent : y – b = m(x – a)

y – 3 = 2(x – 1)

2x – y + 1 = 0

Normal : y - b = -1/m(x - a)

y - 3 = -1/2(x - 1)

x + 2y – 7 = 0