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
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)