Applications of Differentiation - Interpreting Gradients and Concavity

Applications of Differentiation - Interpreting Gradients and Concavity

The diagram below shows the curve \(y = \mathrm{f}'(x)\).

  1. State the \(x\)-coordinates of the stationary points for the curve \(y = \mathrm{f}(x)\). Hence determine the nature of these stationary points.
  2. State the maximal range of values of \(x\) such that the curve \(y = \mathrm{f}(x)\) is
    1. concave downwards,
    2. increasing.

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Answer:(a) \(x=a\): minimum point (b)(i) \(0<x<b\) (ii) \(a\le x<0\) or \(x>0\)

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