show that the intermediate calue theorem applies on the indicated interval and find the value of c in the interval gauranteed by the theorem. round to four decimal places. 2. Show that the Intermediate Value Theorem applies on the indicated interval and find the value of cin the interval guaranteed by the theorem. Round to four decimal places.f(x) = x* – x² + 3x – 1,[0, 1]f(c) = 0

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Description: show that the intermediate calue theorem applies on the indicated interval and find the value of c in the interval gauranteed by the theorem. round to four decimal places. 2. Show that the Intermediate Value Theorem applies on the indicated interval

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.2: Exponential Functions

Problem 58E

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show that the intermediate calue theorem applies on the indicated interval and find the value of c in the interval gauranteed by the theorem. round to four decimal places.

2. Show that the Intermediate Value Theorem applies on the indicated interval and find the value of c
in the interval guaranteed by the theorem. Round to four decimal places.
f(x) = x* – x² + 3x – 1,
[0, 1]
f(c) = 0

Expert Solution

Step 1

$f (x) = x^{4} - x^{2} + 3 x + 1$

we know that f(x) is continuous on the given interval [0,1]

lets find out f(0) when x=0

$f (x) = x^{4} - x^{2} + 3 x - 1 x = 0 f (0) = 0^{4} - 0^{2} + 3 (0) - 1 = - 1 x = 1 f (1) = 1^{4} - 1^{2} + 3 (1) - 1 = 2$

f(0)=-1 and f(1)=2

So there lies a point where the graph of f(x) crosses x axis

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