Cambridge AS & A Level. 2025. Mathematics (9709). May/June - Paper 1 (11) · Pure Mathematics 1 - Question 2

The equation of a curve is such that $\dfrac{dy}{dx} = 4(2x-5)^3 - 9x^{\frac{1}{2}}$. The curve passes through the point $A\left(4, -\frac{11}{2}\right)$.

**(a)** Find the gradient of the normal to the curve at the point *A*.