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Chapter 4 79

# Chapter 4 79 - 10 11 SECTION 4.6 GRAPHING WITH CALCULUS AND...

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Unformatted text preview: 10. 11. SECTION 4.6 GRAPHING WITH CALCULUS AND CALCULATORS 341 minimum at i: f(%) = g — i375 — 10 = —%i ”(23) : 48x — 6 = 6(8m — 1). which is positive (f is CU) on (\$.00) and negative (f isCD) on (—00, é). fhas an [Pat (%,f(—§—)) = (ﬁ—%). 3 3 -1-' 15 20 —6 From the graphs, it appears that f increases on (07 3.6) and decreases on (—00. 0) and (3.6, 00); that f has a local maximum of f(3.6) m 2.5 and no local minima; that f is CU on (5.5, 00) and CD on (—00, 0) and (0, 5.5); and 2 iw+11mi207 11 20 that f has an IP at (5.5.213). f(ac) — \$2 — 1 + a: m2 2 f’(;r) : 7112072 + 40315—3 = —w’3(11m i 40), which is positive (f is increasing) on (07 ﬂ). and negative 40 4O . (f is decreasing) on (—007 0) and on (H, 00). By the FDT, f has a local maximum at as = ﬁ' 40 2 40 ﬂ _ (i) +11(ﬁ) —20 1600+11-11‘40—20‘121 201. .. f( 1) i ———(%)2 _ 1600 —80 ,and f has no local m1n1mum. f’(m) = —11:c_2 + 4095—3 => f"(a:) = 2230—3 — 1201:"4 : 2934013: , 60). which is positive (f is CU) on )) = (6—i«%)- lg (60 00) and negative (f is CD) on (—oo,0) and (0 E). f has an IP at (%.f( it ’11 ._i 1 From the graph, it appears that f increases on (—2.1, 2.1) and decreases on (—3, —2.1) and (2.1. 3); that f has alocal maximum of ﬁll) m 4.5 and a local minimum of f(~2.1) % 74.5; that f is CU on (—3.07 0) and CD on (O, 3.0) and that f has an IP at (07 0). f(a:) = m 9 — 332 => 2 2 , 7m 9729: _ . ., x :——+\/9—ZB2 : —.whlch s ost f() /—9 \$2 *9 x2 1 p live 3 ‘32 2, 37‘5) and negative (f is decreasing) on (—3 ’32‘5) and (3—? 3). By the FDT. . 2 f has a local max1mum value of f<¥) : 3—‘2/21 / 9 — (¥) : g; and f has a local minimum value of (f is increasing) on ( f(_32‘/§> : 73 (since f is an odd function). f’(x) : ¢% + V9 — 902 => f"(\$) ﬂ \/9 — \$2 (722:) + \$26) (9 i \$2)_1/2(_2\$) 110(9 \$2),1/2 , —2:c — 303(9 ~ \$2)‘1 — at 9 i 3:2 _ 1/ 2 9— x 732: 1:3 _ 33(2m2 — 27) i/g — \$2 1 (9 — x2)3/2 _ (9 7 m2)3/2 which is positive (f is CU) on (737 0) and negative (f is CD) on (O, 3). f has an IP at (0. 0). ...
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