Calc Final Exam Review chp2

harryprim's version from 2015-12-09 17:45


Question Answer
T or F? If a function h is continuous at a point x = a, then h must be differentiable at point at x=aFalse, there can be a corner or a cusp.
When can a limit fail to exist?A limit can fail to exist if 1) the right and left limits are not the same, 2) if the function goes to + or - infinity
What is a vertical asymptote?It means that as x->a, f(x)->∞ cannot be touched by function
What is a horizontal asymptote?It is a horizontal line that shows the behavior far off of the graph, can be touched
f is differentiable at a if f'(a) exists
Relationship between differentiability and continuity If f is differentiable, then f is continuous. f may not be differentiable if f is continuous
When is a function not differentiable?If there is a corner or cusp, jump or removable discontinuity, or if there is a vertical tangent
What does f' say about f?If f' is positive, f is inc/ if f' is negative, f is dec. If f'=0, then that is an inflection point for f
What does f'' say about f?If f'' is positive, f is concave up, if f'' is negative, f is concave down
What happens at an inflection point?The concavity of f changes

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