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\[ \mathrm{f}(x)=x^{3}+3 x^{2}-2 \sqrt{x} \quad x>0 \] - Show that \(f(x)=0\) has a root in the interval \([0.6,0.7]\)

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\[
\mathrm{f}(x)=x^{3}+3 x^{2}-2 \sqrt{x} \quad x>0
\]
(a) Show that \(f(x)=0\) has a root in the interval \([0.6,0.7]\)
(b) Find \(\mathrm{f}^{\prime}(x)\)
(c) Staring with \(x_{0}=0.65\), apply the Newton-Raphson procedure once to find an approximate solution to the equation \(\mathrm{f}(x)=0\) giving your answer to 3 decimal places.
in Mathematics by Platinum (102k points) | 365 views

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