Interval bisection and linear interpolationEdexcel International A Level Further Maths: Mind map

Exam questions on Interval bisection and linear interpolation

1. Let $f(x)=x^3+2x-7$ for real $x$.
   Show that the equation $f(x)=0$ has a root in the interval $[1,2]$.2 marks
2. Two functions are defined for real $x$: $f(x)=\frac{1}{x-2}$ (for $x\neq2$) and $g(x)=(x-2)^2$.
   Explain why the change of sign of $f$ between $x=1$ and $x=3$ does not show that $f(x)=0$ has a root in $[1,3]$.2 marks
3. The equation $x^3+x-5=0$ has a single real root $\alpha$. Let $f(x)=x^3+x-5$.
   Use linear interpolation on the interval $[1,2]$ to find a first approximation to $\alpha$.3 marks