Question

Consider the following function. f(x) = 3x − e x i. Plot the graph of the function f(x) in R and identify the interval that the first positive root lies. Write the command(s) that you use and the result(s).

Answer 1

The interval of the function f(x) = 3 · x - eˣ such that the function shall be positive is x ∈ (0.6191, 1.5121).

How to find the interval of a function that cannot be solved for x analytically

In this question we have an expression that combines polynomic and exponential expression, whose variable x cannot be cleared by analytical approaches, but by numerical and graphical methods. Herein we decide to find the interval by graphical methods, using a graphing tool:

First, write the function in explicit form (f(x) = 3 · x - eˣ). Second, find the two points such that the function goes through the x-axis (horizontal axis). Third, define the set of possible x-values by interval notation such that y > 0.

Then, the points of the function that are on the x-axis are (x₁, y₁) = (0.6191, 0) and (x₂, y₂) = (1.5121, 0). Then, the interval of the function f(x) = 3 · x - eˣ such that the function shall be positive is x ∈ (0.6191, 1.5121).

To learn more on functions: brainly.com/question/12431044

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