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WorksheetsApplication of derivatives
Total questions: 15
Worksheet time: 13mins
Name
Class
Date
1.
These are word problems that deal with the application of maximum and minimum value of a function.
a)
Maximizing and Minimizing Problems
b)
Optimization Problems
c)
Pogi Problems
d)
Application Problems
2.
What are the two numbers that will give the maximum product?
a)
40 and 40
b)
20 and 60
c)
45 and 35
d)
30 and 50
3.
If f ′(x) ≥0 , ∀ x∈R then f is
a)
strictly increasing on R
b)
strictly decreasing on R
c)
increasing on R
d)
decreasing on R
4.
The function f(x)= x2−8x+12 is strictly decreasing in
a)
(−∞, ∞)
b)
(2, 6)
c)
(−∞, 4)
d)
(4, ∞)
5.
The min. value of f(x)=x2−6x+5 is
a)
4
b)
-6
c)
6
d)
-4
6.
The maximum and minimum value of 3 sin x + 4 cos x +10 is
a)
17 and 3
b)
15 and 5
c)
12 and 10
d)
None of these
7.
The absolute minimum value of x4 – x2 – 2x+ 5
a)
is equal to 5
b)
is equal to 3
c)
is equal to 7
d)
does not exist
8.
How many extrema are in the picture?
a)
2
b)
3
c)
4
d)
5
9.
Does this graph have a maximum or minimum value?
a)
maximum
b)
minimum
c)
neither
d)
both
10.
Does this graph have a maximum or minimum value?
a)
maximum
b)
minimum
c)
neither
d)
both
11.
If f '(x) <0, what is true about f(x)?
a)
it is concave up there
b)
it's decreasing
c)
It's increasing
d)
it is concave down there
12.
The radius of a circle is decreasing at a constant rate of 0.1 cm/sec. In terms of the circumference C, what is the rate of change of the area of the circle, in square centimeters per second?
a)
-(0.2)πC
b)
-(0.1)C
c)
(0.1)2C
d)
(0.1)2C
13.
If the position of a particle is represented by x(t) = -t2 + 1, what is its instantaneous velocity at t = 1?
a)
v = 0
b)
v = 1
c)
v = -1
d)
v = -2
14.
Over what interval(s) is f(x) decreasing?
a)
(-3, 1)
b)
(-∞, -5) ∪ (0, 2)
c)
(-∞, -3) ∪ (1, ∞)
d)
(-5, 0) ∪ (2, ∞)
15.
Over what interval(s) is f(x) increasing?
a)
before -3 and after 1
b)
between -3 and 1
c)
(-5, 0) ∪ (2, ∞)
d)
(-5, ∞)
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