Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question 11?
Answer should be (-5). Please show work, thank you!
![Figure 3.6
Definition Rate of Change and the Slope of the Tangent Line
The average rate of change in f on the interval [a, x] is the slope of the
corresponding secant line:
msec -
(1)
The instantaneous rate of change in f at a is
f(x) = f(a)
x-a
mtan
lim
x-a
f(x) = f(a)
x-a
"
which is also the slope of the tangent line at (a, f(a)), provided this limit
exists. The tangent line is the unique line through (a, f(a)) with slope mtan. Its
equation is
y = f(a) = mtan(x − a).
. The definition of msec involves a difference quotient, introduced
in Section 1.10.
133
/1184
>](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F627ffe10-a730-4e4c-b7e9-b306478e5985%2Fa728a5f2-204d-4c46-ab7c-3c3c6bfacc66%2Ftzag2ws_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Figure 3.6
Definition Rate of Change and the Slope of the Tangent Line
The average rate of change in f on the interval [a, x] is the slope of the
corresponding secant line:
msec -
(1)
The instantaneous rate of change in f at a is
f(x) = f(a)
x-a
mtan
lim
x-a
f(x) = f(a)
x-a
"
which is also the slope of the tangent line at (a, f(a)), provided this limit
exists. The tangent line is the unique line through (a, f(a)) with slope mtan. Its
equation is
y = f(a) = mtan(x − a).
. The definition of msec involves a difference quotient, introduced
in Section 1.10.
133
/1184
>
Transcribed Image Text:VICT, VITUAL 1000 p/ reprodu
6. The following figure shows the graph of f and a line tangent to the graph of
6. Find f(6) and f'(6).
fat x
УА
9
8
7
6
5-
4
3
2
1
0
-
y=f(x)
1
2 3 4 5 6 7
8
9 X
7. An equation of the line tangent to the graph of f at the point (2, 7) is
y = 4x − 1. Find f(2) and f'(2).
-
-
8. An equation of the line tangent to the graph of g at x = 3 is y = 5x + 4.
Find g(3) and g'(3).
9. If h(1) = 2 and h'(1) = 3, find an equation of the line tangent to the
graph of h at x = 1.
10. If ƒ'(−2) = 7, find an equation of the line tangent to the graph of f at the
point (-2, 4).
11. Use definition (1) (p. 133) to find the slope of the line tangent to the graph
of f(x) = -5x + 1 at the point (1, - 4).
12. Use definition (2) (p. 135) to find the slope of the line tangent to the graph
of f/m) Kot DA FI
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