The vertical height HHH of a roller coaster track, in metres, is modeled by the equation H=H(x),x>0H = H(x), x > 0H=H(x),x>0, where xxx is the horizontal distance from a reference point. The track passes through the point P(4,10)P(4, 10)P(4,10).
Given that
dHdx=3x2−8x\frac{dH}{dx} = \frac{3x^2 - 8}{\sqrt{x}}dxdH=x3x2−8
Find the equation of the tangent to the track profile at PPP, writing your answer in the form y=mx+cy = mx + cy=mx+c, where mmm and ccc are integers to be found.
Find the function H(x)H(x)H(x).
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.