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Home > APCALC > Chapter 5 > Lesson 5.4.1 > Problem 5-146

5-146.

Multiple Choice: Let be the function given by . Which of the following statements about are true?

  1. is continuous at .

  2. is differentiable at .

  3. has an absolute minimum at .

Examples of functions that are not differentiable at . Notice that some of them are still continuous at .

5 first quadrant curves each labeled, f of x, with tick mark labeled, c, on x axis, first increasing concave up ending at closed point x = c, second, same curve, with increasing concave down curve starting at open point x = c, above closed point, third, increasing, changing from concave up to concave down at open point at x = c, fourth, increasing concave up, changing to decreasing curve, concave up, at x = c, fifth, increasing, changing from concave up to concave down at x = c.

The Three Conditions of Continuity

  1. I only

  1. II only

  1. III only

  1. I and III

  1. II and III

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