Find the equation of the tangent and the normal to the following curves at the indicated points:

y = 2x2 – 3x – 1 at (1, – 2)

finding the slope of the tangent by differentiating the curve



m(tangent) at (1, – 2) = 1


normal is perpendicular to tangent so, m1m2 = – 1


m(normal) at (1, – 2) = – 1


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


y + 2 = 1(x – 1)


y = x – 3


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


y + 2 = – 1(x – 1)


y + x + 1 = 0


3