The diagram below shows the curve $y = \mathrm{f}'(x).$ State the $x$-coordinates of the station

Question

The diagram below shows the curve $y = \mathrm{f}'(x).$ State the $x$-coordinates of the stationary points for the curve $y = \mathrm{f}(x).$ Hence determine the nature of these stationary points. State the maximal range of values of $x$ such that the curve $y = \mathrm{f}(x)$ is concave downwards, decreasing.

Accepted Answer

(a) $x=-\sqrt{k}$ and $x=\sqrt{k}$: maximum points (b)(i) $x1$ (ii) $-\sqrt{k}\le x<1$ or $x\ge\sqrt{k}$

Applications of Differentiation - Interpreting Gradients and Concavity

Applications of Differentiation - Interpreting Gradients and Concavity

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