Consider the family of curves given by

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

x y + p y^{2} + q x = 1

, where

p

and

q

are real constants. For the point

(1,1)

on such a curve, which ordered pair

(p,q)

yields a horizontal tangent at that point? (a)

\left(-\dfrac12,\dfrac12\right)

(b)

(-1,1)

(c)

(1,-1)

(d)

(2,-1)