Section 5.2 Extra Practice
STUDENT BOOK PAGES 235–240
1. Determine whether the given function is increasing or
decreasing.
a. y ⫽ 7x
1 3x
b. y ⫽ a b
6
3x
c. y ⫽
22
d. y ⫽ 2x ⫹x
2
e. y ⫽ 0.99x
f. y ⫽ x ⫻ 56x
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2. Differentiate the following functions.
a. y ⫽ 52x
b. y ⫽ 42x⫹1
2
c. y ⫽ 74x ⫹2x
d. y ⫽ 12 ⫻ 54x
e. y ⫽ 25x ⫹ x 5
2
f. y ⫽ 8(x⫺1)
3. Determine the derivative of each of the following
functions.
a. y ⫽ x ⫻ 33x
2
b. y ⫽ 2x ⫻ 4x
c. y ⫽ x 2 ⫻ 103x
3
d. y ⫽ 11x 2 ⫻ 2x ⫹4x
1
3
2
e. y ⫽ ⫻ 5x ⫹x
x
10
f. y ⫽ 10 ⫻ 3x
4. For each function, determine all values of t such that
f ⬘(t) ⫽ 0, if any such values exist.
2
a. f (t) ⫽ 7t
2
b. f (t) ⫽ 20 ⫻ 2(t⫹2)
c. f (t) ⫽ t 2 ⫻ 2t
d. f (t) ⫽ 5t ⫻ 9t
4
e. f (t) ⫽ 2t 2 ⫻ 4t
2
f. f (t) ⫽ 52t ⫹4t
5. Determine the slope of the line tangent to each of the
following functions at the given value of x.
a. y ⫽ 45x, x ⫽ 2
2
b. y ⫽ 10 ⫻ 5x , x ⫽ 4
3
c. y ⫽ 7x ⫻ 4x , x ⫽ 1
d. y ⫽ 3x 4 ⫻ 10x, x ⫽ 0
3
e. y ⫽ x ⫻ 2x ⫹1, x ⫽ 2
2
f. y ⫽ 52x , x ⫽ 0
6. Determine the equation of the line tangent to f (x) at
the given value of x.
3
a. f (x) ⫽ 9x , x ⫽ 1
b. f (x) ⫽ 2 ⫻ 4x, x ⫽ 0
2
c. f (x) ⫽ 2x ⫻ 3x ⫹x, x ⫽ 1
d. f (x) ⫽ x 3 ⫻ 24x, x ⫽ 1
3
e. f (x) ⫽ 2x 3 ⫻ 2x , x ⫽ 1
2
f. f (x) ⫽ 2 ⫻ 10x ⫹5x⫹1, x ⫽ 0
7. The population of a particular town, P, t years after
the time of its establishment can be expressed by
P(t) ⫽ 20 000(1.2) t.
a. What is the initial population of the town?
b. How many people will the town have in 5 years?
What will be the instantaneous rate of change in
the population?
c. How many people will the town have in 20 years?
What will be the instantaneous rate of change in
the population?
d. Do you expect the population to be larger or
smaller in 30 years than in 20 years?
8. Differentiate each of the following functions.
2
a. y ⫽ 3(x⫹5)
2
b. y ⫽ 24x ⫹x⫹10
c. y ⫽ 4⫺3x
4
2
d. y ⫽ 6x ⫹x ⫹1
10
e. y ⫽ 7x ⫹3
x
f. y ⫽ 32
Section 5.2 Extra Practice
389