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Calculus: Early Transcendental Fun...

6th Edition
Ron Larson + 1 other
ISBN: 9781285774770

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Section
BuyFindarrow_forward

Calculus: Early Transcendental Fun...

6th Edition
Ron Larson + 1 other
ISBN: 9781285774770
Textbook Problem

Using the Intermediate Value Theorem In Exercises 91-98, use the Intermediate Value Theorem and a graphing utility to approximate the zero of the function in the interval [ 0 , 1 ] . Repeatedly “zoom in” on the graph of the function to approximate the zero accurate to two decimal places. Use the zero or root feature of the graphing utility to approximate the zero accurate to four decimal places.

f ( x ) = x 4 x 2 + 3 x 1

To determine
Root of given function by graphing utility and confirm the result with intermediate value theorem.

Explanation

Graph:

Explanation:

Given

f(x)=x4x2+3x1

From graph we can observe that f value becomes zero at

x0.37

Hence

x0.37

is approximated root by using graphing utility.

We can confirm this result with intermediate value theorem as follows

Calculations:

Given function f is continuous is continuous on the closed interval [0, 1]

and f(0)=0402+3(0)1=1<0f(1)=14 -12+3(1)-1=2>0

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