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=x3x2−8Find 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).
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.