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# 4th - b Find the local maximum and minimum values of f c...

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RECITATION QUESTIONS MATH 119 (WEEK 4) 1. Find the critical points of the function f ( x ) = | x 2 - 1 | 2. Find the critical numbers of the function a ) g ( x ) = | 2 x + 3 | b ) f ( θ ) = 2 cos θ + sin 2 θ 3. Find the absolute maximum and absolute minimun values of f on the given interval. f ( x ) = sin x + cos x, [0 , π/ 3] 4. Show that the equation 2 x - 1 - sin x = 0 has exactly one real root 5. At what values of x does f have a local maximum or minimum (look at page 247 question 6 in Stewart for the graph of the function ) 6. For the function f ( x ) = x 4 - 2 x 2 + 3 a ) Find the intervals on which f is increasing or decreasing.
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Unformatted text preview: b ) Find the local maximum and minimum values of f . c ) Find the intervals of concavity and the inﬂection points. 7. Evaluate the limit and justify each step by indicating the appropriate properties of limits. a ) lim x →-∞ √ 9 x 6-x x 3 + 1 b ) lim x →-∞ ( x + p x 2 + 2 x ) c ) lim x →∞ x sin 1 x 8. Find the horizontal asymptotes of the curve and use them,together with concavity and inter-vals of increase and decrease ,to sketch the curve y = x x 2 + 1 1...
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