answer d (a) Find all the critical points, extreme values, interval of concavity and the zeros of the functionf(x) = x³ – 3x2 – 4x + 12, and hence sketch the graph of the function.(b) Use L'Hospital's Rule to evaluate the following limits.(i) lim x sin()(ii) lim InzIn(r*+1)(iii) lim(C) For the function f(x) = x° – x, determine whether the hypothesis of Rolle's theorem hold on theinterval [0, 1], and, if it does, verify the conclusion of the Rolle's theorem.(d) Determine whether the hypothesis of the mean value theorem hold for the functionf(x) = 3x? – 5x +1 on the interval [2, 5] and if it does, find a value c satisfying the conclusion ofthe theorem.

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(d) Determine whether the hypothesis of the mean value theorem hold for the function f(x) = 3x2 – 5x +1 on the interval [2,5] and if it does, find a value c satisfying the conclusion of the theorem.

(d) Determine whether the hypothesis of the mean value theorem hold for the function f(x) = 3x2 – 5x +1 on the interval [2,5] and if it does, find a value c satisfying the conclusion of the theorem.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 54E

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Question

answer d

(a) Find all the critical points, extreme values, interval of concavity and the zeros of the function
f(x) = x³ – 3x2 – 4x + 12, and hence sketch the graph of the function.
(b) Use L'Hospital's Rule to evaluate the following limits.
(i) lim x sin()
(ii) lim Inz
In(r*+1)
(iii) lim
(C) For the function f(x) = x° – x, determine whether the hypothesis of Rolle's theorem hold on the
interval [0, 1], and, if it does, verify the conclusion of the Rolle's theorem.
(d) Determine whether the hypothesis of the mean value theorem hold for the function
f(x) = 3x? – 5x +1 on the interval [2, 5] and if it does, find a value c satisfying the conclusion of
the theorem.

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