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Numerical Methods

Numerical Methods

Medium
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Question 2

f(x)=3xex−1f(x) = 3xe^x - 1f(x)=3xex−1. The curve with equation y=f(x)y = f(x)y=f(x) has a turning point PPP.

a.

Find the exact coordinates of PPP.

[5]
b.

The equation f(x)=0f(x) = 0f(x)=0 has a root between x=0.25x = 0.25x=0.25 and x=0.3x = 0.3x=0.3. Use the iterative formula

xn+1=13e−xn x_{n+1} = \frac{1}{3}e^{-x_n} xn+1​=31​e−xn​

with x0=0.25x_0 = 0.25x0​=0.25 to find, to 4 decimal places, the values of x1x_1x1​, x2 x_2\,x2​ and x3x_3x3​.

[3]
c.

By choosing a suitable interval, show that a root of f(x)=0f(x) = 0f(x)=0 is x=0.2576x = 0.2576x=0.2576 correct to 4 decimal places.

[3]
Markscheme

Numerical Methods Questions

  1. A Level
  2. /Old Maths
  3. /Numerical Methods

7 exam-style questions on Edexcel A Level Old Maths Numerical Methods. Each one has a worked solution and a mark scheme showing where the marks go.

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