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FFObjective: The student will discuss continuity and differentiability of functions.
Use the overhead provided. Use Quick Pole to ask Always Sometimes Never questions. Make sure to use the presenter so that class discussion can take place after each question.
At a later date, give the Learn Check with the same concepts.
1. If the function is continuous at x = c, then the limit exists as x EMBED Equation.3 c.
2. If the value of the function exists at x = c, then the function is differentiable at x = c.
3. If the derivative equals 0 at x = c, then f(x) has a local minimum at x = c.
4. If the function is not continuous at x = c, then the function is differentiable at x = c.
5. If the function is nondifferentiable at x = c, then the function is continuous at x = c.
6. If the value of the function does not exist at x = c, then the function is not continuous at x = c.
7. If the function is differentiable at x = c, then the limit exists as x EMBED Equation.3 c.
8. If the function has a corner point at x = c, then the function is differentiable at x = c.
9. If f(x) has a local maximum at x = c, then the derivative equals 0 at x = c.
10. If f(x) has an absolute minimum at x = c, then the function has a corner point at x = c.
11. If the function is continuous at x = c, then the value of the function exists at x = c.
12. If the function is continuous at x = c, then the function is differentiable at x = c.
13. If the limit exists as x EMBED Equation.3 c, then the function is continuous at x = c.
14. If the limit does not exist at x EMBED Equation.3 c, then the function is differentiable at x = c.
15. If the limit exists as x EMBED Equation.3 c, then the value of the function exists at x = c.
16. If the function is nondifferentiable at x = c, then the function has a vertical tangent at
x = c.
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