Applications of Differentiation - Interpreting Gradients and Concavity

Applications of Differentiation - Interpreting Gradients and Concavity

State the maximal range of values of \(x\) for which the graph of \(y = \mathrm{f}(x)\) is

  1. strictly decreasing,
  2. decreasing,
  3. concave upwards,
  4. concave downwards.

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Answer:(a) \((-\infty,1)\) and \((1,\infty)\), separately. (b) \((-\infty,1)\) and \((1,\infty)\), separately. (c) \(x>1\). (d) \(x<1\).

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