Question

For each of the following questions, consider a function, f(x) that is continuous on [a,b]. How...

For each of the following questions, consider a function, f(x) that is continuous on [a,b].

  1. How would you find the critical values of f(x)? Explain.

  2. Where would f(x) be increasing/decreasing? Explain.

  3. At what possible x values would f(x) have extrema? Explain.

  4. Is it possible that f(x) is continuous and has no extrema on the interval [a,b]? Use the Extreme Value Theorem to explain your response.

  5. If f’’(c) = 0, c in (a,b), and f’’(x) > 0 for all x values in (a,c) and (c,b), is it possible for the point (x,f(c)) to be an inflection point? Explain.

  6. Explain how one would use the following tests:

1st Derivative Test:

2nd Derivative Test:

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