business calculus exam
phaha
Math1250-17Exam2S202.pdf
Math 1250-17 Name: _________________________ Mr. W.O. Griffith Exam 2 F’20 Score: _____ / 100
Answer each of the following to the best of your ability. Four points per problem.
1) Find the derivative of the function ( ) 3 28 2 4f x x x= − + + .
a.
b.
c.
d.
e. none of the above
2) Find the slope of the tangent line to the graph of the function ( ) 23 8f x x= − − at 2x = − .
a. 12
b. –3
c. –8
d. –12
e. none of the above
3) Find the derivative of the function ( ) 6
10 f x
x =
−
a.
b.
c.
d.
e. none of the above
4) Find the derivative of the function ( ) 6
5h x x= .
a.
b.
c.
d.
e.
5) Determine the point(s), (if any), at which the graph of 4
108 4y x x= − + has a horizontal tangent.
a. 0
b. 0 and 3
c. 0 and –3
d. 3
e. There are no points at which the graph has a horizontal tangent.
6) Find the marginal revenue, measured in dollars, for producing x units for ( ) 250 0.5R x x x= − .
a. 50 x− dollars
b. 50 x+ dollars
c. 50 dollars
d. 50 .5x− dollars
e. 50 .5x+ dollars
7) Find the derivative of the function ( ) 3
6
3
x x f x
+ = .
a.
b.
c.
d.
e.
8) Use the given information to find ( )2f of the function ( ) ( ) ( )f x g x h x= . ( )2 3g = , ( )2 2g = − ,
( )2 1h = − and ( )2 4h = .
a.
b.
c.
d.
e.
9) Find the derivative of the function ( ) ( ) 65
1 6f x x x= + .
a.
b.
c.
d.
e.
10) Use the demand function 2
325 1 7 2
p x
p
= −
+ to find the rate of change in the demand x for the given
price 400p = . Round your answer to two decimal places.
a. 1.44 units per dollar
b. –0.72 units per dollar
c. 0.72 units per dollar
d. 0.96 units per dollar
e. –1.44 units per dollar
11) Find dy
dx of y u= and
2 6u x= + .
a.
b.
c.
d.
e. none of these choices
12) True or false: if ( ) ( )y f x g x= then ( ) ( )y f x g x = .
a. True
b. False
13) Find the second derivative of the function ( ) 4
73f x x= .
a.
b.
c.
d.
e. None of the above
14) Identify the open intervals where the function ( ) 24 4 1f x x x= + + is increasing or decreasing.
a. decreasing:
1 ,
2
−
; increasing: 1
, 2
−
b. increasing:
1 ,
2
−
; decreasing: 1
, 2
−
c. increasing on ( ),−
d. decreasing on ( ),−
e. none of the above
15) Find all critical numbers of 3 2
3 24 5y x x x= − − + .
a. 0x =
b. 4 and 2x x= − = −
c. 4 and 2x x= − =
d. 2 and 4x x= − =
16) Find the relative minima of 3 2
3 45 19y x x x= − − + .
a. ( )3, 100−
b. ( )5, 156−
c. ( )3, 116−
d. ( )5, 44−
e. no relative minima
17) Find the x-values of all relative maxima of 3 21
5 24 2 3
y x x x= − + + .
a. 0x =
b. 6x =
c. 5x =
d. 4x =
e. no relative maxima
18) (Counts as Two Questions) For the function ( ) = − +3 22 24 4f x x x find:
(a) Find the critical numbers of f (if any);
(b) Find the open intervals where the function is increasing or decreasing; and
(c) Apply the First Derivative Test to identify all relative extrema.
a. (a) 0 and 8x =
(b) increasing: ( ) ( ), 0 8, ;− ; decreasing: ( )0, 8
(c) relative max: ; relative min:
b. (a) 0 and 8x =
(b) decreasing: ( ) ( ), 0 8, ;− increasing: ( )0, 8
(c) relative min: ; relative max:
c. (a) 0 and 1x =
(b) increasing: ( ) ( ), 0 1, ;− decreasing: ( )0, 1
(c) relative max: ( )0 4f = ; relative min: ( )1 18f = −
d. (a) 0 and 1x =
(b) decreasing: ( ) ( ), 0 1, ;− increasing: ( )0, 1
(c) relative min: ( )0 4f = ; relative max: ( )1 18f = −
e. (a) 0 and 1x =
(b) increasing: ( ) ( ), 0 1, ;− decreasing: ( )0, 1
(c) relative max: ( )0 4f = ; relative min: no relative min.
19) Find all relative maxima of 4 3 2
8 16 6y x x x= − + + .
a. ( )0, 6
b. ( )2, 22
c. ( )4, 6
d. ( )0, 6 and ( )4, 6
e. no relative maxima
20) Determine the open intervals on which the graph of ( ) 27 6 6f x x x= − + is concave downward or concave upward.
a. concave upward on ( ), 0− ; concave downward on ( )0,
b. concave downward on ( ),−
c. concave upward on ( ),−
d. concave downward on ( ), 0− ; concave upward ( )0,
e. concave upward on ( ), 1− ; concave downward on ( )1,
21) Find all relative extrema of the function 2
4 5x x− − − . Use the Second Derivative Test where
applicable.
a. relative max: ( )2 1f − = −
b. relative min: ( )0 5f = −
c. no relative min
d. no relative max
e. both A and C
f. both B and D
22) Find all relative minima of 4 3 2
16 18y x x x= − + + .
a. ( )0, 18
b. ( )2, 34
c. ( )4, 18
d. ( )0, 18 and ( )4, 18
e. no relative maxima
23) Find the x-value at which the function 3 21
5 24 2 3
y x x x= − + + has a point of inflection.
a. 0x =
b. 6x =
c. 5x =
d. 4x =
e. no point of inflection
24) The graph of f is shown in the figure. Sketch a graph of the derivative of f.
a.
b.
c.
d.
