How do you find the roots of the equation f(x)=e-x-(x+4)/5 without a graph?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 44RE
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How do you find the roots of the equation f(x)=e-x-(x+4)/5 without a graph?

Expert Solution
Step 1

Note that intersection of line and exponential curve is a single point which is root of those two. The root of f(x)=e-x-(x+4)/5 can be computed as follows.

f(x)= e _(x+4)
5
f(0.1) e01-0.1 0.08 (+ve value)
5
-0.02 (-ve value
(0.2)= e02 (0.2+4)
f(0.2) 6
22
5
This implies that the root lies between 0.1 and 0.2
(0.15+4)
0.1 0.2
- s(0.15)- e
-0.15
0.03 (+ve value)
2
5
The root lies between 0.15 and 0.2
(0.175+4)0.004 (+ve value)
0.15 0.
=f(0.175)
-0.175
= e
22
2
5
The root lies between 0.175 and 0.2
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