# extenssion

Education

18

All Questions

14

Multiple Choice

0

True False

4

Essay

0

Short Answer

0

Not Answered

Q 1

Let M represent the absolute maximum of f(x)in an interval. Let R represent a root of f(x)in the given interval.
Let m represent the absolute minimum of f(x)in the interval.
If ,then which of the following is true over the closed interval ?
A)M and R occur at a critical point and m occurs at an endpoint.
B)M and m occur at critical points.
C)M,m,and R occur at endpoints of the given interval.
D)M occurs at an endpoint,whereas m and R occur at a critical point.

Free

Multiple Choice

A

Q 2

What value of c in the open interval (0,16)satisfies the Mean Value Theorem for ?
A)0
B)
C)
D)4

Free

Multiple Choice

C

Q 3

If ,then on which interval(s)is the continuous function f(x)increasing?
A)
B)
C)
D)

Free

Multiple Choice

A

Q 4

The points of inflection for are at and .Which of the following is (are)true?
I)The points of inflection for are at and .
II)The points of inflection for are at and .
III)The points of inflection for are at and .
A)I only
B)II only
C)I and II only
D)I and III only

Multiple Choice

Q 5

The graph of f ′(x)is given below for .On which interval(s)is the function f(x)both increasing and concave up?
A)
B)
C)
D)

Multiple Choice

Q 6

A farmer has 225 yards of fencing to form two identical rectangular pens and a third pen that is twice as long as the other two pens,as shown in the diagram below.All three pens have the same width,x.Which value of y produces the maximum total fenced area?
A)
B)15
C)
D)

Multiple Choice

Q 7

For the function ,how many of the inflection points of the function are also extrema?
A)3
B)2
C)1
D)None

Multiple Choice

Q 8

The position of an object moving along a straight line for is given by ,and the position of a second object moving along the same line is given by .If both objects begin at ,at what time is the distance between the objects a minimum?
A)2
B)
C)
D)0

Multiple Choice

Q 9

Given the following conditions for ,which graph best illustrates ? : The domain of the function is the real numbers,but ;
; ; .
for all x where ,and does not exist at . for , for ,and does not exist at .
A)
B)
C)
D)

Multiple Choice

Q 10

A calculator may be used for the following question.Let be a function such that .In the interval ,the graph of has a point of inflection nearest .
A)0.37
B)1.233
C)2.141
D)2.268

Multiple Choice

Q 11

For time ,a particle moves along the x-axis with position given by .During what time intervals is the speed of the particle increasing?
A) < t ≤ 10 only
B)0 ≤ t < 1 and < t <
C)0 ≤ t < 1 and < t ≤ 10
D)1 < t < and
< t ≤ 10

Multiple Choice

Q 12

For time ,a particle moves along the x-axis with position given by .What is the position of the particle when it is farthest to the left?
A)
B)-11
C)-16
D)

Multiple Choice

Q 13

Based on the graph of pictured above,how many points of inflection exist for the twice differentiable function on the interval ?
A)4
B)3
C)2
D)1

Multiple Choice

Q 14

A rectangle is drawn in the first quadrant so that it has two adjacent sides on the coordinate axes and one vertex on the curve .Find the x coordinate of the vertex for which the area of the rectangle is a maximum.
A)
B)
C)
D)

Multiple Choice

Q 15

The function is defined as on the open interval (-3,3)as illustrated in the graph shown.
-Determine the coordinates of the relative extrema of in the open interval (-3,3).

Essay

Q 16

Let be defined as in the open interval (-3,3).Determine the coordinate(s)of the relative maxima of in the open interval.Explain your reasoning.

Essay

Q 17

For what values of x is not defined? Explain your reasoning.

Essay

Q 18

Find all values of x for which is concave down.Explain your reasoning.

Essay