Theory question 104
DifferentiationFind the equation of the normal to the curve y = 7x − 5x2 at x = 2.
Show the model answer
Model answer
At x = 2: y = 14 − 20 = −6.
dy/dx = 7 − 10x = −13 at x = 2, so the normal has gradient 1/13.
y + 6 = (1/13)(x − 2), i.e. x − 13y − 80 = 0.
Explanation
The normal is perpendicular to the tangent: m(normal) = −1/m(tangent).