Theory question 103
DifferentiationThe normal to the curve y = 2x2 + x − 3 at the point (2, 7) meets the x-axis at point P. Find the coordinates of P.
Show the model answer
Model answer
dy/dx = 4x + 1 = 9 at x = 2 (gradient of tangent)
Gradient of normal = −1/9
Normal: y − 7 = −(1/9)(x − 2), i.e. x + 9y − 65 = 0
On the x-axis y = 0, so x = 65
P is (65, 0)
Explanation
The normal is perpendicular to the tangent, so its gradient is −1/(dy/dx).