Applications of Differentiation - Interpreting Gradients and Concavity
Applications of Differentiation - Interpreting Gradients and Concavity
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,
- strictly increasing,
- decreasing.
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Answer:(a) \(x=-1\) stationary point of inflexion, \(x=3\) maximum (b)(i) \(x<-3\) or \(-1<x<1\) or \(x>1\) (b)(ii) \(1<x<3\) (b)(iii) \(x<-3\) or \(-3<x<1\) or \(x\ge3\)
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