What does different limits information tell us about the features of a function?
Where the instantaneous rate of change is zero
Where the instantaneous rate of change does not exist
At the endpoints of the interval of interest
Where the function value is zero
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F(x) must approach negative infinity somewhere in the interval [a,b]
F(x) must have a discontinuity on [a,b]
F(a) must be greater than f(b)
F(x) must have a maximum on the interval [a,b]
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The Intermediate Value Theorem
The Mean Value Theorem
The Extreme Value Theorem
Rolle's Theorem
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The absolute minimum value is 0.
The absolute maximum value is 14/3.
There is a relative minimum between x=–5 and x=–4.
There is one point which is a relative maximum where the instantaneous rate of change is zero.
The instantaneous rate of change does not exist at x=–3 and there is a relative maximum there.
(1,1) is a relative maximum point.
The left end point is a relative maximum.
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