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Calculus true-false

The following statements are either true or false.

a). If x=p is not a critical point of f, then x=p is not a local maximum of f.

b). If x=p is not a local maximum of f, then x=p is not a critical point of f.

c). If f'(x) is continuous and f(x) has no critical points, then f is everywhere increasing or everywhere decreasing.

d). If f''(x) is continuous and the graph of f has an inflection point at x=p, then f''(p) = 0.

Solution Preview

a) true - all local maximums are critical points

b) false - a critical point can also occur at the ...

Solution Summary

This shows how to determine if a set of statements regarding calculus functions are true or false.

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