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Test Chapter 3 Graphing M121 Form A
Name _______________________________ Date ________________
Show all work for credit.
1. Use the first derivative to find all relative extrema (max/min) for f(x) = 2x(x –4)3 . {you will
need to factor out the least powers) Show number sign chart Circle the (x,y) coordinates of
any answers
2. Find the points of inflection for y = 5×4 – x5
Show number line sign chart Circle answer(s)
3. Sketch and label (extrema and points of inflection) for the graph of a function having the
following characteristics:
f(0) = 2 f(2) = 0
f’(x) chart:
f(1) = 1 x = 3 is a vertical asymptote Horizontal asymptote: y=0
+
–
+
0
f’’(x) chart:
+
2
–
0
+
1
3
+
2
+
3
4. Sketch the Graph ( labeling all extrema and inflection points) (Show number line analysis
for f’(x) and f’’(x)}
f(x) = x4 – 4×3
Step 1 f’(x) =
Step 2 f’’(x) =
Step 3 Table
Step 4 sketch
!
5. Sketch: ( ) = ‘( + 1)! + 2
{label any extrema and points
of inflection}
= ___________ (rewrite)
Step 1 f ‘ =
f ‘ number line
Step 2 f ‘ ‘ =
f ‘ ‘ number line
Step 3 Table
Step 4 Sketch and Label
6. Find the Critical numbers of the first Derivative for =
(#$%)”
#”
7. Find the critical numbers for the second derivative when
first derivative is
′ = (
$!#
#$%)!
8. Find the absolute max/min of y = 2×3 – 9×2 +12x on the
interval [-1,4]
!”#
9. Sketch and label extrema and points of inflection: ( ) = ! !
Need number line analysis for both derivatives.
Vertical asymptote
x = ____
Horizontal asymptote y = _____
Step 1:
f’(x) =
$%(#$!)
f ‘ number line
f ‘ ‘ ( x)
=
!(#$’)
##
f ‘ ‘ number line
Step 3 Table
Step 4 Sketch and label
#!
show limit needed
10. Sketch and Label
: ( ) =
!# ”
(#$%)”
{Label extrema and points of inflection}
Note: The second derivatives is already given. You need to show work for the first
derivative. Use number line analysis for each derivative.
VA ________
HA _________ Show limit
Step 1:
Find ( = (
$)#
#$%)!
!
Step 2: Second derivative
(( ( ) =
)(!#*%)
(#$%)#
!!
Step 3: Table
Step 4 Sketch and label
11. Use implicit differentiation to find dy/dx for
when x = 1 and y = 2
{Uses product rule)
xy2 + y3 = 10
Bonus For the profit function ” − 10 # = ” , (p = profit in dollars) Find how rapidly the
profit P is growing when sales ( x = # items sold) is growing by 10 items per day and when the
number of items sold is 2 and when profit p = $4. Hint: take the derivative of both sides with
respect to t = time in days.
(write the units of the dp/dt in your answer)
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