Find the equation of the tangent to the curve with equation
y=16x3−9x12 y = \frac{1}{6}x^3 - 9x^\frac{1}{2} y=61x3−9x21at the point P(9,94.5)P(9, 94.5)P(9,94.5).
Give your answer in the form ax+by+c=0ax + by + c = 0ax+by+c=0, where aaa, bbb and ccc are integers.
The curve with equation y=f(x)y = f(x)y=f(x) also passes through the point P(9,94.5)P(9, 94.5)P(9,94.5). Given that
f′(x)=16x3−9x12 f'(x) = \frac{1}{6}x^3 - 9x^\frac{1}{2} f′(x)=61x3−9x21find f(x)f(x)f(x), giving the coefficients in simplest form.
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions 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), matched to the AQA A Level Maths (7357) 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.
