The equation of tangent at (2, 3) on the curve y² = px³ + q is y = 4x - 7. Find the values of ‘p’…

$p = 2$, $q = -7$. The point $(2, 3)$ lies on the curve: $9 = 8p + q$ ... (1) $2y\frac{dy}{dx} = 3px^2$, so the slope at $(2, 3)$ is $\frac{3p(4)}{2(3)} = 2p$. The slope of the tangent $y = 4x - 7$ is $4$, so $2p = 4$ and $p = 2$. From (1): $q = 9 - 16 = -7$.