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Calculus Review (Limits, Derivatives, Max-Min) Flashcards | StudBud
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Calculus Review (Limits, Derivatives, Max-Min)
Calculus Review (Limits, Derivatives, Max-Min)
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1
What does the second derivative tell you about a function?
Vertical Asymptote
Horizontal \Asymptote
Locate inflection points
Critical Points
2
Assume that f(x)=√x
2
+3. Find the slope of a tangent line between the points at x = 2 and x = 3.
.818
-.196
.213
1.228
3
What is the derivative of 10x
5
?
50x5
15x4
50x4
5x4
4
What is f''' of 2x
4
- 4x
3
+ 5x + 7
48x - 24
24x2 - 24
48x -12
8x3 - 12x2 + 12
5
What is the derivative of 8x
2
y
3
?
16x(y3) + 8x2((3y2)y'x)
(16x)(3y2)(y'x)
16x(y3) + 8x2((3x2)y'x)
16x2(3y2) + (y'x)
6
Find the derivative of f(x) = 2e
4x+1
.
(8e4x+1)(4x+1)
2e4x+1
8xe4x+1
8e4x+1
7
What is the limit at x=1?
Limit = ∞
limit = 4
Limit = 2
Does Not Exist
8
Find the derivative of f(x) = (x
2
+ 3)(x
3
- 3x + 1).
5x4 + 2x - 9
x4 - 6x2 - 2x + 9
-x4 + 6x2 + 2x - 9
5x4 - 2x - 9
9
Find critical numbers and determine if they are a local min or max from f(x) = x
2
+ 5x - 1.
(-5±√21)/2, max
-5/2, max
(-5±√21)/2, min
-5/2, min
10
I need a box without a lid that before being folded is 9inx6in. What is the correct Volume equ?
(2x-9)(2x-6)(x)
(9-x)(x)(6-x)
(9-2x)(6-2x)(x)
(9-6)x<span style="font-size: 11px;">3</span>
11
Find the derivative of 4(2x-9)
4
.
4(2)4
16(2x-9)3(2)
16(2)3
4(2x-9)3(2)
12
What is the inflection point of x
3
+ 2x
2
- 3?
-2/3
3/4
4
6
13
Where is (x
2
+ 4x +4)/(x+2) discontinuous?
x = 4
x = -2
x = 2
x = 0
14
What is the derivative of sec x?
(sec x)2
-csc x cot x
sec x tan x
(-csc x)2
15
Is x
4
+ 3x
2
- 4 increasing, decreasing, or neither?
Decreasing
Increasing then decreasing
Neither
Increasing
16
Is the function x
3
+ 5 increasing, decreasing, or neither between [1,∞]?
Undefined
Increasing
Neither
Decreasing
17
lim
x
→
0
(1/x
2
)
0
Does Not Exist
∞
1/x
18
What is the slope of a line with coordinates at (3,4) and (5,12)?
-4
4
1/4
9
19
A radius is changing at 4cm/sec at what rate is the area growing? What are we solving for?
dc/dt
dA/dt
dv/dt
dr/dt
