Concept explainers
Newton’s Method In calculus you will learn that if
is a polynomial function, then the derivative of is
Newton’s Method is an efficient method for approximating the (or real zeros) of a function, such as . The following steps outline Newton’s Method.
STEP 1: Select an initial value that is somewhat close to the being sought.
STEP 2: Find values for using the relation
until you get two consecutive values and that agree to whatever decimal place accuracy you desire.
STEP 3: The approximate zero will be .
Consider the polynomial .
a. Evaluate and .
b. What might we conclude about a zero of ? Explain.
c. Use Newton’s Method to approximate an , , , of to four decimal places.
d. Use a graphing utility to graph and verify your answer in part .
e. Using a graphing utility, evaluate to verify your result.
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Precalculus Enhanced with Graphing Utilities, Books a la Carte Edition Plus NEW MyLab Math -- Access Card Package (7th Edition)
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