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3 Unit A2 1: Pure Mathematics (A-level only)

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Question 208

Let f(x)=x3−x−1f(x)=x^3-x-1f(x)=x3−x−1.

a.

Show that f(x)=0f(x)=0f(x)=0 has a root between 1.3 and 1.4.

[2]
b.

Starting with x0=1.3x_0=1.3x0​=1.3, use Newton–Raphson iteration to find x1x_1x1​, x2 x_2\,x2​ and x3x_3x3​. Give each value to six decimal places.

[4]
c.

By considering a suitable interval, prove that the root is 1.3247 correct to four decimal places.

[3]
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3 Unit A2 1: Pure Mathematics (A-level only) Questions

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