Use intermediate theorem to explain P [x] = x* – x' – 10 has a zero in [2, 3]

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Use intermediate theorem to explain P [x] =
x - x- 10 has a zero in [2, 3]
Transcribed Image Text:Use intermediate theorem to explain P [x] = x - x- 10 has a zero in [2, 3]
Expert Solution
Step 1

According to intermediate value theorem of a function f(x) is continuous on [a, b] and L is any number between f(a) and f(b) then there must be a value x= c where a<c<b such that f(c) =L.

Here the given function is P(x) = x4—x3—10

Since the given function is a polynomial function, we know that all polynomial functions are continuous everywhere so the given polynomial function is also continuous on [2,3]. So here we can use intermediate value theorem.

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