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WorksheetsMNTHS Calculus Mid Term MC sections
Total questions: 15
Worksheet time: 53mins
Name
Class
Date
1.
Derivative means the same thing as
a)
slope of the tangent line
b)
slope of the normal line
c)
exponent
d)
potato
2.
Find the derivative.
a)
sinx
b)
-sinx
c)
tanx
d)
-tanx
3.
find x such that f'(x)=0 for f(x) = 3x2 - 5x
a)
x = 0
b)
x = 1/6
c)
x = 5/6
d)
x = 6/5
4.
What is the limit?
a)
Infinity
b)
20
c)
DNE
d)
12
5.
a)
Does not exist
b)
6
c)
4
d)
3
6.
Meghan is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the ladder sliding down the wall when the tip of the ladder is 5 ft high?
a)
3 ft/sec
b)
-7.2 ft/sec
c)
7.2 ft/sec
d)
12
7.
Where is the graph not differentiable?
a)
x = -2, -1, 0, 1
b)
x = -2, -1, 1
c)
x = -2, -1
d)
x = -1,
8.
Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 4 cm/min. How fast is the area of the pool increasing when the radius is 10 cm?
a)
86π cm2/min
b)
89π cm2/min
c)
80π cm2/min
d)
71π cm2/min
9.
If y=2x-8, what is the minimum value of the product xy?
a)
-16
b)
-8
c)
-4
d)
2
10.
We want to construct a box whose base length is 3 times the base width. If the box must have a volume of 50 ft3, determine the dimensions that will minimize the amount of material used.
a)
w=2.027ft, h=4.055ft, l=6.082ft
b)
w=1.488ft, h=3.347ft, l=6.694ft
c)
w=2.231ft, h=3.347ft, l=6.694ft
d)
w=0.485ft, h=2.111ft, l=4.222ft
11.
Over what interval(s) is f(x) decreasing?
a)
(-3, 1)
b)
(-∞, -5) ∪ (0, 2)
c)
(-∞, -3) ∪ (1, ∞)
d)
(-5, 0) ∪ (2, ∞)
12.
If (a,b) is a local minimum, then what will be true about f'(a)?
a)
It's positive
b)
It's negative
c)
It's zero
d)
Cannot be determined
13.
If (a,b) is a local maximum, then what will be true about f''(a)?
a)
It's positive
b)
It's negative
c)
It's zero
d)
Cannot be determined
14.
For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.
a)
increasing
b)
decreasing
c)
concave up
d)
concave down
15.
Given the following graph of f', the derivative of f. For what x-value does f have a relative minimum?
a)
x=-1 and x=4
b)
x=-3
c)
x=1
d)
x=3
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