Standard +0.3 This is a straightforward application of the linear interpolation formula with given endpoints. Students need to evaluate f(0.7) and f(0.8), then apply the standard formula. While it involves a transcendental function (tan), the method is mechanical and requires no problem-solving insight—just careful arithmetic and formula recall. Slightly easier than average due to its routine nature.
$$f(x) = 3x^2 + x - \tan \left( \frac{x}{2} \right) - 2, \quad -\pi < x < \pi.$$
The equation \(f(x) = 0\) has a root \(\alpha\) in the interval \([0.7, 0.8]\).
Use linear interpolation, on the values at the end points of this interval, to obtain an approximation to \(\alpha\). Give your answer to 3 decimal places.
[4]
$$f(x) = 3x^2 + x - \tan \left( \frac{x}{2} \right) - 2, \quad -\pi < x < \pi.$$
The equation $f(x) = 0$ has a root $\alpha$ in the interval $[0.7, 0.8]$.
Use linear interpolation, on the values at the end points of this interval, to obtain an approximation to $\alpha$. Give your answer to 3 decimal places.
[4]
\hfill \mbox{\textit{Edexcel FP1 Q43 [4]}}