Connections Between Function Features And Limits
What does different limits information tell us about the features of a function?
- 1.Select all the places to look for extreme points (maxima, minima):
- A.
Where the instantaneous rate of change is zero
- B.
Where the instantaneous rate of change does not exist
- C.
At the endpoints of the interval of interest
- D.
Where the function value is zero
- 2.Which of the following must be true if a function f(x) does not have a minimum on an interval [a,b].
- A.
F(x) must approach negative infinity somewhere in the interval [a,b]
- B.
F(x) must have a discontinuity on [a,b]
- C.
F(a) must be greater than f(b)
- D.
F(x) must have a maximum on the interval [a,b]
- 3.Which existence theorem allows use to use guess-and-check to solve equations which can be written in the form F(x) = 0 for a continuous function F?
- A.
The Intermediate Value Theorem
- B.
The Mean Value Theorem
- C.
The Extreme Value Theorem
- D.
Rolle's Theorem
- 4.
Select all the correct statements about extreme points of the function in the graph.- A.
The absolute minimum value is 0.
- B.
The absolute maximum value is 14/3.
- C.
There is a relative minimum between x=–5 and x=–4.
- D.
There is one point which is a relative maximum where the instantaneous rate of change is zero.
- E.
The instantaneous rate of change does not exist at x=–3 and there is a relative maximum there.
- F.
(1,1) is a relative maximum point.
- G.
The left end point is a relative maximum.
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