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# 7th - Math 119 Recitation 7 November 1 2006 1 Verify that...

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Math 119 Recitation 7 November 1, 2006 1. Verify that the function f ( x ) = sin(2 πx ) satisﬁes (a) f is continuous on [ - 1 , 1], (b) f is diﬀerentiable on ( - 1 , 1), (c) f ( - 1) = f (1). and ﬁnd all numbers c ( - 1 , 1) such that f 0 ( c ) = 0. 2. Verify that the function f ( x ) = 3 x ) satisﬁes (a) f is continuous on [0 , 1], (b) f is diﬀerentiable on (0 , 1), and ﬁnd all numbers c ( - 1 , 1) such that f 0 ( c ) = f (1) - f (0) 1 - 0 . 3. Show that the equation 2 x - 1 - sin x = 0 has exactly one real root. 4. Given f ( x ) = x 2 x +3 , (a) ﬁnd intervals on which f is increasing or decreasing. (b) ﬁnd the local maximum and minimum values of f . (c) ﬁnd the intervals of concavity and the inﬂection points.
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