The derivative as a gradient and rate of changeEdexcel International A Level Maths: Mind map

Exam questions on The derivative as a gradient and rate of change

1. A curve has equation $y=x^2+3x$. The point $P$ has coordinates $(2,10)$ and the point $Q$ on the curve has $x$-coordinate $2+h$, where $h\neq0$.
   Explain why the gradient of the chord $PQ$ is not equal to the gradient of the tangent at $P$, and how the gradient of the tangent can be found from it.2 marks
2. The volume $V$ cm$^3$ of water in a tank at time $t$ minutes is modelled by $V=40+6t-0.5t^2$ for $0\le t\le10$.
   Find the time at which the volume of water momentarily stops changing, and explain what the sign of $\frac{\mathrm{d}V}{\mathrm{d}t}$ tells you about the volume just before this time.2 marks
3. The curve $y=f(x)$ has equation $f(x)=x^3-6x^2+9x+2$.
   Find $f'(x)$ and hence solve $f'(x)=0$.3 marks