Section 5.1 Extra Practice
STUDENT BOOK PAGES 227–234
1. Determine the derivative of each of the following.
a. f (x) ⫽ 5e 4x
e 6x ⫹ e 20
b. f (x) ⫽
2
x
c. f (x) ⫽ 12e 3
d. f (x) ⫽ 2e 3x ⫹1
2
e. f (x) ⫽ e x ⫹3x
2
f. f (x) ⫽ e (x⫺2)
Copyright © 2009 by Nelson Education Ltd.
2. For each function, determine the value of the
derivative f ⬘(a) for the given value of a.
a. f (x) ⫽ x 2 ⫹ e 2x, a ⫽ 4
e 4x
b. f (x) ⫽ , a ⫽ 1
42
c. f (x) ⫽ e 3x ⫺8x⫹1, a ⫽ 3
4 5
d. f (x) ⫽ e x , a ⫽ 0
5
2
e. f (x) ⫽ e (x⫹1) , a ⫽ 2
3
ex
f. f (x) ⫽ ⫺3x , a ⫽ 1
e
3. Find the slope of the line tangent to y ⫽ e x
for each of the following values of x.
a. x ⫽ ⫺1
b. x ⫽ 1
c. x ⫽ 2
d. x ⫽ 0
2
5. Determine y⬘, y⬙ and y⵮ for the following functions.
a. y ⫽ 6e ⫺x
x2 ⫹ 1
b. y ⫽ e 2
x
c. y ⫽ e 2
d. y ⫽ (e x ⫹ 1) 2
6. For each of the following functions, determine the
points at which the tangent line is horizontal, if any
such points exist.
3
a. f (x) ⫽ e x
b. f (x) ⫽ e ⫺2x
x
c. f (x) ⫽ 4e 2
2
d. f (x) ⫽ e (x ⫹5)
e. f (x) ⫽ 2xe 2x
7. The population, P, of bacteria in a sample at
time t (in hours) can be expressed by
t
P(t) ⫽ 5000A20 ⫹ e⫺30 B.
a. What is the initial population of bacteria?
b. What is the rate of change at time t?
c. What is the rate of change at time t ⫽ 5?
d. What is the rate of change at time t ⫽ 20?
⫺1
4. Determine the equation of the line tangent to each
of the functions at the point where x ⫽ a.
3x
a. f (x) ⫽ e⫺ 2 , a ⫽ 2
2
b. f (x) ⫽ 8e x , a ⫽ 1
2
c. f (x) ⫽ x , a ⫽ ⫺1
e 2
d. f (x) ⫽ e (x ⫹x), a ⫽ 0
⫺2
e. f (x) ⫽ e x , a ⫽ 2
f. f (x) ⫽ 10 ⫹ e x, a ⫽ 10
Section 5.1 Extra Practice
387