Exercise 3.3
Exercise 3.3
Exercise 3.3
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MA111: Prepared by Dr.Archara Pacheenburawana 32<br />
• Use the above information to sketch the graph.<br />
(a) f(x) = 2x 3 −3x 2 −12x (b) f(x) = x 4 −6x 2<br />
(c) f(x) = 3x 5 −5x 3 +3 (d) f(x) = x √ x 2 +1<br />
(e) f(x) = x 1/3 (x+3) 2/3 (f) f(x) = sin 2 x<br />
Answer to <strong>Exercise</strong> 3.5<br />
1. (a) CU on (−∞,−1)∪(1,∞); CD on (−1,1)<br />
(b) CU on (−∞,0); CD on (0,∞)<br />
(c) CU on (1,∞); CD on (−∞,1)<br />
(d) CU on (−1,0)∪(1,∞); CD on (−∞,−1)∪(0,1)<br />
2. (a) Inc. on (−∞,−1)∪(2,∞); dec. on (−1,2); loc. max. f(−1) = 7;<br />
loc. min. f(2) = −20; CU on ( 1,∞); CD on (−∞, 1); IP 2 2 (1 2 ,−13)<br />
2<br />
y<br />
−10<br />
5<br />
1<br />
x<br />
−20<br />
(b) Inc. on (− √ 3,0)∪( √ 3,∞); dec. on (−∞,− √ 3)∪(0, √ 3);<br />
loc. min. f(± √ 3) = −9; loc. max. f(0) = 0; CU on (−∞,−1)∪(1,∞);<br />
CD on (−1,1); IP (±1,−5)<br />
y<br />
−1<br />
1<br />
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x<br />
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−10<br />
(c) Inc. on (−∞,−1)∪(1,∞); dec. on (−1,−1); loc. max. f(−1) = 5;<br />
loc. min. f(1) = 1; CU on (−1/ √ 2,0)∪(1/ √ 2,∞);<br />
CD on (−∞,−1/ √ 2)∪(1/ √ 2,∞); IP (0,3), (±1/ √ 2,3∓ 8√ 7 2)