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Question 508

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)=x5​12​+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,

a.

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,

[3]
b.

find f(x)f(x)f(x).

[5]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, 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. Each one has a worked solution and a mark scheme showing where the marks go.

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