A metal worker is crafting a sculpture where the upper profile is defined by the curve with equation
y=15x2−12x y = \frac{1}{5}x^2 - \frac{12}{\sqrt{x}} y=51x2−x12at the point Q(4,−2.8)Q(4, -2.8)Q(4,−2.8).
Find the equation of the tangent to this profile at point QQQ.
Give your answer in the form ax+by+c=0ax + by + c = 0ax+by+c=0, where aaa, bbb and ccc are integers.
The lower profile of the sculpture, given by the curve with equation y=f(x)y = f(x)y=f(x), also passes through the point Q(4,−2.8)Q(4, -2.8)Q(4,−2.8). Given that
f′(x)=15x2−12x f'(x) = \frac{1}{5}x^2 - \frac{12}{\sqrt{x}} f′(x)=51x2−x12find the expression for f(x)f(x)f(x), giving the coefficients in simplest form.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions 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, 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.
