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).
864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.