1.16: Estimate roots using a graph

Figure 2 shows the graph of $y=x-\dfrac1{2x^2}$ for $0.4\le x\le5$ drawn on a grid.

(a) (i) Express $x-\dfrac1{2x^2}$ as a single fraction.

(ii) Hence use the graph to obtain, to one significant figure, an estimate for the value of $\sqrt[3]{0.5}$. (3)

(b) By drawing a suitable straight line on the grid, find an estimate to 2 significant figures, for the root of the equation

in the interval $0.4\le x\le5$. (3)