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# HW5 - f x = x p 9-x 2 Problem 5 1 2 True or false...

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MATH 102, ASSIGNMENT 5 DUE JUNE 20 Problem 1. Find the relative and the absolute extrema for f ( x ) = x + 1 x on the interval [ . 25 , 2 ] . Then do the same problem for the interval [ - 2 , 2 ] . Problem 2. Sketch the graph a function having all of the following characteristics: f ( 0 ) = f ( 2 ) = 0; f 0 ( x ) < 0 if x < 1, f 0 ( x ) > 0 if x > 1, f 0 ( x ) = 0 if x = 1 f 00 > 0 Problem 3. Let f and g be concave upwards on the interval [ 0 , 1 ] . True or False: f + g is concave upwards on [ 0 , 1 ] . True or False: f - g is concave upwards on [ 0 , 1 ] . If True, justify. If False, give an example. Problem 4. Consider the following function: f ( x ) = x 9 - x i) Find the relative extrema of f using the First-Derivative Test. ii) Find the relative extrema of f using the Second-Derivative Test. iii) Find the absolute extrema of f . Problem 5. Same questions as in Problem 4, this time for
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Unformatted text preview: f ( x ) = x p 9-x 2 . Problem 5 1 2 . True or false: Mathematics is to the scientist and the engineer a tool, to the professional mathematician a religion, but to the ordi-nary person a stumbling block. [. ..] What we ﬁnd difﬁcult about mathematics is the formal, symbolic presentation of the subject by pedagogues with a taste for dogma, sadism and incomprehensible squiggles. (J.E. Gordon in Structures or Why Things Don’t Fall Down ) J-RULE: Just answers - “yes”, “5” - won’t get you full marks, but (correctly) justiﬁed answers - “yes, because. ..”, “(some algebra). .. (sweat sweat) . .. 5” - will. 1...
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