The table below gives for the value of continuous function f at each x-value. Using the Intermediate Value Theorem and the information in the table, determine the smallest interval in which the function must have a root. x f(x) -5 1.25 -4-1.03 -3-3.05 -2-4.01 -1-4.02 0 -4.69 1-4.43 2-5.45 3 -0.76 4 -4.93 5 -9.93

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Transcribed Image Text:Answer (in interval notation):
The table below gives for the value of continuous function f at each x-value. Using the Intermediate Value
Theorem and the information in the table, determine the smallest interval in which the function must have a
root.
x f(x)
-5 1.25
-4-1.03
-3-3.05
-2-4.01
-1-4.02|
0 -4.69
1-4.43
2-5.45
3 -0.76
4 -4.93
5 -9.93
Transcribed Image Text:The table below gives for the value of continuous function f at each x-value. Using the Intermediate Value Theorem and the information in the table, determine the smallest interval in which the function must have a root. x f(x) -5 1.25 -4-1.03 -3-3.05 -2-4.01 -1-4.02| 0 -4.69 1-4.43 2-5.45 3 -0.76 4 -4.93 5 -9.93
Expert Solution
Step 1

Introduction: 

The intermediate value theorem is a theorem about continuous functions. Intermediate value theorem has its importance in Mathematics, especially in functional analysis. This theorem explains the virtues of continuity of a function.

Given:

Value table.

To Find:

smallest interval  containing zero.

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