Consider the function. f(x) = 2/x (a) Compute the slope of the secant lines from (0, 0) to (x, f(x)) for x = 1, 0.1, 0.01, 0.001, 0.0001. (Use decimal notation. Give your answer to five decimal places.) For x = 1:

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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Consider the function.
f(x) = 2/x
(a) Compute the slope of the secant lines from (0, 0) to (x, f(x)) for x = 1, 0.1, 0.01, 0.001, 0.0001.
(Use decimal notation. Give your answer to five decimal places.)
For x =
1:
For x = 0.1:
For x = 0.01:
For x = 0.001:
Transcribed Image Text:Consider the function. f(x) = 2/x (a) Compute the slope of the secant lines from (0, 0) to (x, f(x)) for x = 1, 0.1, 0.01, 0.001, 0.0001. (Use decimal notation. Give your answer to five decimal places.) For x = 1: For x = 0.1: For x = 0.01: For x = 0.001:
For x = 0.0001:
(b) Select the correct statement about the tangent line.
The tangent line will be vertical because the slopes of the secant lines increase.
The tangent line does not exist.
There is not enough information to draw a conclusion.
The tangent line is horizontal.
(c) Plot the graph of and verify your observation from part (b).
f(x) =
y
+
LO
Transcribed Image Text:For x = 0.0001: (b) Select the correct statement about the tangent line. The tangent line will be vertical because the slopes of the secant lines increase. The tangent line does not exist. There is not enough information to draw a conclusion. The tangent line is horizontal. (c) Plot the graph of and verify your observation from part (b). f(x) = y + LO
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