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Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640

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BuyFindarrow_forward

Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640
Textbook Problem

In Exercises 75-78, (a) show that the function f is continuous for all values of x in the interval [a, b] and (b) prove that f must have at least one zero in the interval (a, b) by showing that f(a) and f(b) have opposite signs.

75. f(x) = x2 − 6x + 8; a = 1, b = 3

(a)

To determine

To show: The given function is continuous in the interval [1,3] .

Explanation

Proof:

The given function is f(x)=x26x+8 .

As f(x) is polynomial of degree 2, it is continuous everywhere

(b)

To determine

To show: If f(a) and f(b) have opposite signs. then there have at least one value c for which f(c) equals zero.

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