(See Solution) Let f be a function that is continuous on the interval [0,6). The function f is twice differentiable except at x=3. The function f and its derivatives


Question: Let \(f\) be a function that is continuous on the interval [0,6). The function \(f\) is twice differentiable except at \(x=3\). The function \(f\) and its derivatives have the properties indicated in the table below, where DNE indicates that the derivatives of \(f\) do not exist at \(x=3\).

  1. For \(0
  2. For \(0
  3. Let \(h\) be the function defined by \(h(x)=\int_{1}^{x} f(t) d t\) on the open interval \((0,6)\). For \(0
  4. For the function \(h\) defined in part (c), find all values of \(x\), for \(0
  5. Sketch a graph of \(f\) on \([0,6)\) that displays all of the properties indicated in the table at the top of the page.

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