Applications of Differentiation

Applications of Differentiation

The diagram shows the graph of \(y=\mathrm{f}(x)\), which has a minimum point at \((-3,-3)\). The curve is such that both the \(x\) and \(y\)-axis are asymptotes, and \(y=-2x\) is an oblique asymptote.

  1. State the range of values of \(x\) for which \(\mathrm{f}\) is decreasing.

  2. Sketch the graph of \(y=\mathrm{f}'(x)\).

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Answer:(a) \(x\le-3\) or \(x>0\) (b) See graph.

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