The normal to the curve (y = 2x^{2} + x – 3) at the point (2, 7) meets the x- axis at the point P. Find the coordinates of P.
Explanation
(y = 2x^{2} + x – 3)
(frac{mathrm d y}{mathrm d x} = 4x + 1)
At (2, 7), the gradient is (4(2) + 1 = 9)
The gradient of normal = (-1 div 9 = frac{-1}{9})
Equation of the normal = (y – 7 = frac{-1}{9}(x – 2))
(9y – 63 = 2 – x)
At the point of meeting the x- axis, y = 0
(0 – 63 = 2 – x implies x = 65)
The coordinate of P = (65, 0).