The vertical profile of a survey drone is modeled by a curve CCC with equation h=f(t)h = f(t)h=f(t), t>0t > 0t>0, where hhh is the altitude in meters and ttt is the time in seconds. The drone passes through the point P(4,10)P(4, 10)P(4,10).
Given that f′(t)=3t+2−16t2\displaystyle f'(t) = 3\sqrt{t} + 2 - \frac{16}{t^2}f′(t)=3t+2−t216
Find the equation of the normal to CCC at PPP. Write your answer in the form at+bh+c=0at + bh + c = 0at+bh+c=0, where aaa, bbb and ccc are integers to be found.
Find f(t)f(t)f(t).
Practise Edexcel A Level Maths 11.1 Integrating Standard Functions with exam-style questions for A Level Maths. 81 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.