Finding a curve from its gradientEdexcel International A Level Maths: Mind map

Exam questions on Finding a curve from its gradient

1. A curve passes through the point $(2,9)$ and has gradient function $\dfrac{\mathrm{d}y}{\mathrm{d}x}=3x^2-4x+1$.
   Find the value of $y$ on the curve when $x=-1$.2 marks
2. The gradient of a curve at the point $(x,y)$ is given by $\dfrac{\mathrm{d}y}{\mathrm{d}x}=\dfrac{8}{x^3}-3\sqrt{x}$ for $x>0$. The curve passes through the point $(1,4)$.
   Find the value of $y$ on the curve when $x=4$.2 marks
3. The curve $y=f(x)$ has gradient function $f'(x)=(2x+3)(x-1)$ and passes through the point $(3,10)$.
   Show that $f(x)=\frac23x^3+\frac12x^2-3x+c$, where $c$ is a constant.3 marks