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Chapter 4 5

# Chapter 4 5 - 31 32 33 34 35 36 37 38 39 41 42 SECTION 4.1...

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Unformatted text preview: 31. 32. 33. 34. 35. 36. 37. 38. 39. 41. 42. SECTION 4.1 MAXIMUM AND MINIMUM VALUES 267 f(\$) = 5332 + 4m :> fβ(m)210;r + 4. fβ(z) 2 0 2 a: 2 βΒ§. so β% is the only critical number. ftcc)=w3+ac2βw => f/(x)23x2+2mβ1. fβ(e)=0 2 (m+1)(3mβ1)20 => m=β1.Β§. These are the only critical numbers. f(m) = e3 + 39:2 β 24:1: 2 f/(at) = 33:2 + 62: β 24 2 3(332 + 2x β 8). f'(:c) 2 0 2> 3(m + 4)(:c β 2) 2 0 2 a: 2 41. 2. These are the only critical numbers. m 2 #. Neither of these is a real number. Thus. there are no critical numbers. 803) = 35* +4253 β 6t2 2 sβ(t) : 121:3 +12r2 212:. 5'(t) : 0 2 1225(232 + t β 1) 2 : Oor t2 + t β 1 2 0. Using the quadratic formula to solve the latter equation gives us a 2 _ 4 _1 a 21:: 5 t : 1i 1 (1X ) : 1 i β5 2 0.618. β1.618. The three critical numbers are 0, 4. 2(1) 2 2 2 2 z+1 z +Z+1)12(z+1)(2z+1) 22 -22 f(Z):2ββ β5 fβ(Z)β( 2 2 β 2 220 βiβ Z+Z+1 (z +z+1) (z +z+1) 2(2 + 2) 2 0 2> z 2 0. β2 are the critical numbers. (Note that 22 + z + 1 2 0 since the discriminant < 0.) 2mβlβ3 trapβ320 2 rfar>βg 9(w)=12\$+3|: . => β(ILβ : . 3 ~(2m+3)1f2mββ3<0 221fcc<βΒ§ gβ(ac) is never 0. but gβ(:c) does not exist for :1: 2 β%. so ~g is the only critical number. ()_ 1/3_ β2/3 :> /()_1 β2/3+g β5/3_l β5/3( +2)_\$+2 gac2a: x 932233: 32: 23:0 :1: 23%,)β. gβ(~2) 2 0 and gβ(0) does not exist, but 0 is not in the domain of 9, so the only critical number is 22. g(t) 2 5152/3 + t5/3 2 gβ(t) 2 13913β1/3 + 319/3. g/(O) does not exist. sot 2 0 is a critical number. gβ(t) 2 Β§t_1/3(2 + t) 2 0 42 t 2 β2. sot 2 ~2 is also a critical number. 1 g(t) 2 x/{(1 β t) 2 151/2 β 753/2 2 gβ(t) 2 m β gο¬. gβ(0) does not exist. sot 2 Dis a critical number. , 1 β 3t 1 1 . . . 0 β g (t) 2 2 ο¬ t 2 5. sot 2 3 is also a critical number. F(\$) 2\$4/5(xβ4)2 => F'(m)2x4/5-2(xe4)+(1ββ4)2-Emil/52Γ©wβl/5(x~4)[5-m-2+(\$β4)-4] m~414mβ16 2mβ4 7xβ8 : % 2 % 2 OWhenm2 4. %;and F'(0) does not exist. Critical numbers are 0. g. 4. C(m) = V3 3:2 β m 2 G'(:c) 2 %(IL'2 ~ are) 32β (2w ~1). G'(a:) does not exist when \$2 β :2: 2 0. that is. when w 2 0 or 1. Gβ(m) 2 0 <2 23: β 1 2 0 <2 w 2 %. So the critical numbers are x 2 0.1.1. to ...
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