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Calculus Midterm Review (Derivatives with Apps)
Find the interval(s) of decreasing.
What is f '''(x)?
Calculus Midterm Review (Derivatives with Apps)
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Answers
1
What is f '''(x)?
6+cosx
sinx
6-cosx
cosx
2
Find the interval(s) of decreasing.
(-∞, -2] and [2, ∞)
(-∞, 0] and [0, ∞)
(-∞, ∞)
[-2, 2]
3
The average velocity over an interval of time is the slope of the _______ line.
normal
curved
tangent
secant
4
Find dydx.
-2x/y
-2xy
-x/y
x/y
5
What is the value of the local max?
-16
2
16
-2
6
Find dy/dx.
(2x + 3sinx)/cosy
(2x + 3cosx)/siny
(2x - 3sinx)/cosy
(2x - 3cosx)/siny
7
On what interval(s) is f(x) concave up?
(-∞, 0]
[0, ∞)
(-∞, 0)
(0, ∞)
8
Where does the point of inflection occur in f(x)?
There is no point of inflection.
x = 0
(0, 0)
y = 0
9
Let f(5) = 7, f '(5) = -3, g(5) = 2, g'(5) = 6 and h(x) = 4f(x). What is h'(5)?
28
12
-28
-12
10
The instantaneous velocity at a point in time is the slope of the _______ line.
tangent
secant
curved
normal
11
Find dy/dx.
e4x
4
4ex
4e4x
12
On what interval(s) is f(x) concave down?
[0, ∞)
(-∞, 0)
(0, ∞)
(-∞, 0]
13
Find y'.
1/x
4
4ln4x
4/x
14
Find the interval(s) of increasing.
(-∞ , ∞)
[-2, 2]
(-∞ , 0] and [0 , ∞)
(-∞ , -2] and [2 , ∞)
15
Find dy/dx.
y/x
-x/y
-y/x
x/y
16
What is f ''(x)?
cosx
6-cosx
sinx
6+cosx
17
Find y'.
(2x3 + 3x2)e2x
3x2e2x
2x3e2x
2x3 + 3x2
18
What is f '(x)?
6-cosx
cosx
6+cosx
sinx
19
What is the slope of the normal line to the function at x=1?
-2
1/2
2
-1/2
20
Find dy/dx.
2(cos4x)
2(cos4x)(sin4x)-1/2
2(sin4x)-1/2
4(cos4x)(sin4x)-1/2
21
Acceleration is the second derivative of what?
itself
position
speed
velocity
22
Find y'.
-3(x2 - 1)(x2 + 1)2
-3/(x2 + 1)
-3(x2 - 1)(x2 + 1)-2
(x2 - 1)(x2 + 1)2
23
Find dy/dx.
7(2x2 + 5)6
28x(2x2 + 5)6
4x
4x(2x2 + 5)6
24
Let f(5) = 7, f '(5) = -3, g(5) = 2, g'(5) = 6 and h(x) = f(x) ⋅ g(x). What is h'(5)?
-36
-48
36
48
25
What is the slope of the tangent line to the function at x=1?
4x3 - 2
-2
0
2
