Question: The function f has a derivative everywhere and just one critical point at x = 3. In parts (a)-(d) you are given additional conditions. In each case decide whether x = 3 is a local maximum, a local minimum or a neither. Explain your reasoning. Sketch the graph for all cases

1. \(f'\left( 1 \right)=3\) and \(f'\left( 5 \right)=-1\)
2. \(f\left( x \right)\to \infty \) as \(x\to \infty \) and as \(x\to -\infty \)

(d) \(f'\left( 2 \right)=-1,f\left( 3 \right)=1,f\left( x \right)\to 3\) as \(x\to \infty \).

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