Applications of Differentiation - Interpreting Gradients and Concavity

Applications of Differentiation - Interpreting Gradients and Concavity

Given that the coordinates of \(A\) and \(B\) are \( \left(a,0 \right) \) and \( \left(b,2 \right) \) respectively.
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) \(0<x<b\) (b) \(0<x\le b\) (c) \(x\in\mathbb R,\ x\ne0\) (d) \(\varnothing\)

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