The equation of a curve is $y = 2x^2 + 5$. Find the set of values of $x$ for which \(y 3x^2

Question

The equation of a curve is $y = 2x^2 + 5$. Find the set of values of $x$ for which $y > 3x^2$ and represent this set on a number line.[4] The line $y-kx =3$ is a tangent to the curve at then point P. Find the possible values of $k$.[4] Given that $k > 0$, find the coordinates of P.[3]

Accepted Answer

(a)$-\sqrt 5 < x$ $<\sqrt 5$ (b)$k=\pm 4$ (c)P: (1,7)

2025 SJI PRELIMS P2 Q5

2025 SJI PRELIMS P2 Q5