The altitude hhh (in meters) of a specialized research drone during a 10-second test flight is modeled by the function
h(t)=t3−kt2+15t−12 h(t) = t^3 - kt^2 + 15t - 12 h(t)=t3−kt2+15t−12where t t\,t is the time in seconds (0≤t≤100 \le t \le 100≤t≤10) and k k\,k is a constant.
Find, in simplest form, (i) h′(t)h'(t)h′(t) (ii) h′′(t)h''(t)h′′(t)
The curve with equation v=h′(t)v = h'(t)v=h′(t) (velocity) intersects the curve with equation a=h′′(t)a = h''(t)a=h′′(t) (acceleration) at the points P P\,P and QQQ.
Given that the ttt-coordinate of P P\,P is 5,
find the value of kkk.
Hence find the coordinates of QQQ.
Practise AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
