A specialized drone's vertical displacement from a reference altitude, hhh (in meters), is modeled by the function h(t)=at3+3t2+bt−10h(t) = at^3 + 3t^2 + bt - 10h(t)=at3+3t2+bt−10 where t t\,t is the time in seconds since the drone began its descent and a a\,a and b b\,b are constants.
When h(t)h(t)h(t) is divided by (t−3)(t - 3)(t−3), the remainder is 44.
Use the remainder theorem to show that 9a+b=99a + b = 99a+b=9
Given also that (t+1)(t + 1)(t+1) is a factor of h(t)h(t)h(t),
find the value of a a\,a and the value of bbb.
Find h′(t)h'(t)h′(t).
Hence find the exact coordinates of the stationary points of the curve with equation y=h(t)y = h(t)y=h(t).
Practise Edexcel A Level Maths 1.5 Algebraic Division with exam-style questions for A Level Maths. 65 questions, matched to the Edexcel A Level Maths (9MA0) 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.