题目

Problem

The equation of a curve is such that $\dfrac{dy}{dx}=4x-3\sqrt{x}+1$ .

(a) Find the $x$ -coordinate of the point on the curve at which the gradient is $\dfrac{11}{2}$ .

[3]

(b) Given that the curve passes through the point $(4,11)$ , find the equation of the curve.

[4]

题目中文翻译

一条曲线满足 $\dfrac{dy}{dx}=4x-3\sqrt{x}+1$ 。

(a) 求曲线上斜率为 $\dfrac{11}{2}$ 的点的 $x$ 坐标。

(b) 已知该曲线经过点 $(4,11)$ ，求曲线方程。

CIE 9709 2024 November Paper 11 Q5