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.
480 exam-style questions on AQA A Level Maths 1.11 H: Integration, covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.