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Unformatted text preview: x = 4 r 1 3 is a maximum. Since y = x 1 + x 4 is an odd function, it has point symmetry about the origin. ∴ the stationary point at x =4 r 1 3 is a minimum. Week 3 Version 1 Class 3. 1 3 x + 1 > 1 2 x3 Critical Points: 3 x + 1 = 0 and 2 x3 = 0 ⇒ x =1 3 and x = 3 2 Equality: 1 3 x + 1 = 1 2 x3 ⇒ 3 x + 1 = 2 x3 ⇒ x =4 Draw a number line and test points in each region: Figure 1: Number Line x =5 : 114 > 113 : TRUE x =1 : 12 > 15 : FALSE x = 0 : 1 1 > 13 : TRUE x = 2 : 1 7 > 1 1 : FALSE 1 3 x + 1 > 1 2 x3 has solutions1 3 < x < 3 2 and x <4 4. For x > , e xex < e x , since ex > 0 for all x ∈ R . ⇒ ln( e xex ) < x ⇒ ln( e xex )ln 2 < xln 2 ⇒ ln ± e xex 2 ² < xln 2 ⇒ ln(sinh x ) < xln 2 as required....
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This document was uploaded on 03/19/2012.
 Three '11

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