16A-FinalSample1

# 16A-FinalSample1 - f 00 x and then • Find inﬂection...

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Math 16A, Spring 2010 Final Sample 1 Analyze a function, and sketch the graph of that fct, means extract all the informations we can, by using the technique developed in this class. That’s the road map you may use. Domain x and y intercept Continuity (and classify disc. points) HA and VA derive the fct (ﬁnd f 0 ( x )) and then Study diﬀerentiability Find critical points (keeping in mind the diﬀerence between the case f 0 ( c ) = 0 ﬂat tg line, and f 0 ( c ) =undef. vertical tg line cusp or node) Find increasing ( f 0 > 0) and decreasing ( f 0 < 0) interval Individuate rel max and min by using ﬁrst derivative test derive the fct two times (ﬁnd

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Unformatted text preview: f 00 ( x )) and then • Find inﬂection points • Find concave up ( f 00 > 0) and concave down ( f 00 < 0) interval • Check that the second derivative tests matches with the rel max and min you found previously Use these info the sketch the graph. 1 1. Analyze the function y = x 4-4 x 3 + 5 2. Analyze the function y = ± x 2 + 1 x < 1 4-2 x x ≥ 1 3. Analyze the function y = x + sin ( x ) in the interval I = [0 , 6 π ], and ﬁnd the abs extrema. 4. Find the slope of the tangent line to function f ( x ) = p sin ( πx 2 ) cos 2 ( πx ) in the point ( 1 2 ,f ( 1 2 )) 2...
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16A-FinalSample1 - f 00 x and then • Find inﬂection...

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