A curve has equation y=f(x)y = f(x)y=f(x), where
f′′(x)=12x5+4x,x>0 f''(x) = \frac{12}{\sqrt{x^5}} + 4x, \quad x > 0 f′′(x)=x512+4x,x>0The point P(1,−2)P(1, -2)P(1,−2) lies on the curve.
Given that f′(x)=1f'(x) = 1f′(x)=1 at point PPP,
find the equation of the normal at PPP, writing your answer in the form y=mx+cy = mx + cy=mx+c, where mmm and ccc are constants,
find f(x)f(x)f(x).
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.
