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DERIVATIVES AND GRAPHS

If f'(x)<0 on an interval then f is increasing on that interval
True
False
A critical number of a function f is a number c in the domain of f such that either f'(x)=0 or f'(x) does not exist.
True
False
If f has a local maximum or minimum at c then c is a critical number of f
True
False
If f'(x) does not change signs at c, then:
F has a local maximum or minimum at c
F has no critical number at c
F has no local maximum or minimum at c
None of the above
If f'(x) changes from positive to negative at c then f has a local minimum at c.
True
False
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