Mathematics A H230: Differentiation Topical Past Paper Questions

A man P runs in a straight line from O to A, leaving O at time t = 0. At time t seconds his velocity $ v_{ms}^{-1} $ is given by $ v = 5 + 0.003t^{2} $. Another man $Q$ runs from $O$ to $A$ at a constant speed of $7.08\,\mathrm{m\,s}^{-1}$, starting 5 seconds after $P$. (a) Show…

The diagram shows the curve C with equation $ y = 4x^{2} - 10x + 7 $ and two straight lines, $ l_{1} $ and $ l_{2} $. The line $ l_{1} $ is the normal to C at the point $ \left(\frac{1}{2}, 3\right) $. The line $ l_{2} $ is the normal to C at the minimum point of C. (a) Determine…

The quadratic polynomial $ 2x^{2}-3 $ is denoted by $ f(x) $. Use differentiation from first principles to determine the value of $ f'(2) $.