CC+MATH+1021+2.6+LA
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Clemson University *
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Course
1020
Subject
Mathematics
Date
Apr 3, 2024
Type
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4
Uploaded by GrandWren4158
MATH 1020 Rate of Change function graphs Learning Activity 2.6 Section: ___ Group Number: _______
Score: ______/20 Name: _________________________________ Credit is only given for group work to those present on
all days LA is worked in class. Much of the work we have done so far has been at a specific point P and the derivative values at a point have been numbers – slopes of the tangent lines. By examining a function at various selections for the point, it should be easy to see that the value of the derivative varies at different points. The slopes of the tangent lines as they change along a curve are the output values of a new FUNCTION called the derivative. Graphically we can sketch the derivative function based on the idea that the derivative at any given point P is the slope of the tangent line at point P. Source of graphs: Briggs Calculus 1. (3 pts)
On the graph below, use the labeled points A, B, C, D, E to answer the questions that follow. a. Circle the points where the slope of the curve is negative? A B C D E b. Circle the points where the slope of the curve is positive? D E c. Rank the five given points from least slope to greatest slope. (Hint: the graph has greater steepness
at point A than at point C.) John
Allensworth
C
·
C
,
E
,
A
,
1
,
MATH 1020 Rate of Change function graphs Learning Activity 2.6 2. (2 pts)
Match the graph of each function in (a)-(c) with the graph of its derivative in I-III. (a) (b) (c) I.
II. III.
3.
(3 pts)
Match the graph of each function in (a)-(c) with the graph of its derivative in I-III. (a)
(b)
(c)
I
#
#
A
C
6
I
#
I
MATH 1020 Rate of Change function graphs Learning Activity 2.6 4.
(2 pts)
Choose the graph that depicts the slope graph of the function. a. b. c. d. 5. (4 pts)
Fill in the blank in each sentence below to describe a feature on a slope graph given a feature on its corresponding
function graph
. Choose from: “be increasing”, “be decreasing”, “lie above the x-axis”, or “lie below the x-axis”, “zero”, “positive”, “negative”, “relative max or min”, “inflection point”, “vertical asymptote”, “horizontal asymptote”, “hole”, “jump”
a)
If a continuous and differentiable function !(#)
has a relative minimum
at # = 1
, then its slope graph must
have a/an _______________ at # = 1
. b)
If a continuous and differentiable function
’(#)
has an inflection point
at # = −2
, then its slope graph
must
have a/an _________________ at # = −2
. c)
If a continuous function
ℎ(#)
has a vertical tangent
at # = 0
, then its slope graph
has ______________________ at # = 0
. d)
If a continuous and differentiable function
,(#)
is decreasing
on the interval (0,10), then its slope graph
must
________________ on the interval (0,10). e)
If a continuous and differentiable function
,(#)
is concave up
on the interval (0,10), then its slope graph must
_______________ on the interval (0,10). 6.
(2 pts)
Choose the graph that depicts the slope graph of the function. a. b. c. d. C
inflection
point
relative
max
or
min
horizontal
asymptote
be
concave
dowe
be
increasing
·
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MATH 1020 Rate of Change function graphs Learning Activity 2.6 7.
(4 pts)
Consider the graph of !(#)
below and complete the statements that follow. a. The graph of
!(#)
has a slope of zero at approximately # = ______________.
A tangent line to !(#)
will be horizontal at approximately # = ______________.
The graph of !′(#)
will have a(n) _______________ at these #
value(s). b. The graph of !(#)
is increasing on the interval(s) __________________. The graph of !′(#)
will be ________ on these interval(s). c. The graph of !(#)
is decreasing on the interval(s) __________________. The graph of !′(#)
will be ________ on these interval(s). d. The graph of
!(#)
has an inflection point at approximately # = ______________.
At this inflection pt. the function !(#)
is increasing/decreasing most/least rapidly. Circle appropriately.
The graph of !′(#)
will have a(n) _______________ at this #
value. e. The graph of !(#)
is concave up on the interval(s) __________________. The graph of !′(#)
will be ________ on these interval(s). f. The graph of !(#)
is concave down on the interval(s) __________________. The graph of !′(#)
will be ________ on these interval(s). g.
Choose the graph below that depicts the slope graph of the above function.