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