(ii) If f'(x)< 0 for all xe(a,b), then f is a decreasingEXERCISE 3.31. Verifyf (x)= 2x² -8x+6 defined over thethatthefunctioninterval [1, 3] satisfies the conditions ofRolle's theorem. Find all points cguaranteed by Rolle's theorem.2. For the following exercises, determinewhether the Mean Value Theorem appliesfor the functions over the given interval[a, b]. Justify your answer.3(a) f(x)=x'over [0,2](b) y=x'+2x+1 over [0,6](c) f(x)=(x-1)" over [0,2]

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Answered: 1. Verify f(x)= 2x² -8x+6 defined over…

1. Verify f(x)= 2x² -8x+6 defined over the that the function interval [1, 3] satisfies the conditions of Rolle's theorem. Find all points c guaranteed by Rolle's theorem.

Intermediate Algebra

10th Edition

ISBN:9781285195728

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter8: Conic Sections

Section8.2: More Parabolas And Some Circles

Problem 63.1PS

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Question

(ii) If f'(x)< 0 for all xe(a,b), then f is a decreasing
EXERCISE 3.3
1. Verify
f (x)= 2x² -8x+6 defined over the
that
the
function
interval [1, 3] satisfies the conditions of
Rolle's theorem. Find all points c
guaranteed by Rolle's theorem.
2. For the following exercises, determine
whether the Mean Value Theorem applies
for the functions over the given interval
[a, b]. Justify your answer.
3
(a) f(x)=x'over [0,2]
(b) y=x'+2x+1 over [0,6]
(c) f(x)=(x-1)" over [0,2]

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