Use Newton's Method to Approximate the Indicated Root Of $x ^ { 4 } + x - 4 = 0$

question 66

Short Answer

Use Newton's method to approximate the indicated root of $x ^ { 4 } + x - 4 = 0$ in the interval $[ 1,2 ]$ , correct to six decimal places. Use $x _ { 1 } = 1.5$ as the initial approximation.

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Definitions:

Input-validation Loop

A programming construct used to repeatedly request input from the user until the input meets certain validation criteria.

Condition-controlled Loop

A loop that executes as long as a specified condition remains true.

Valid Range

The set of values that a variable or expression is legally allowed to take within a program.

Expression

A combination of variables, constants, and operators that the programming language evaluates to produce a value.