A curve has equation y=f(x)y = f(x)y=f(x), where
f′′(x)=12x5+4x,x>0f''(x) = \frac{12}{\sqrt{x^5}} + 4x, \quad x > 0f′′(x)=x512+4x,x>0
The 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 Edexcel A Level Maths 11.1 Integrating Standard Functions with exam-style questions for A Level Maths. 81 questions, 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.