ase the one alternative that best completes the statement or answers the questio
ID: 2886244 • Letter: A
Question
ase the one alternative that best completes the statement or answers the question. 1) 1) The cost of a computer system increases with increased processor speeds. The cost C of a system as MHz Find the processor speed for which cost is at a minimum Round to the nearest tenth if D) 0.3 MHz a furnction of processor speed is estimated as C 62-5s+1400, where S is the processor speed in A) 04 M? B) 8.3 MHz C) 33 MHz 2) The total cost to produce x units of perfume is C(x)=(3x+9)(6x+6). Find the marginal average 2)- cost function. 54 2 A) 18 - B) 18x +72,54 C) 36x+72 72 D) 36-4 3) Which of the following is (are) true of f(x) x4-x3? Q0) is an inflection point (II) 15,-?an (II) (0 fO) is a relative minimum point 2' 16 s an inflection point IV) f is increasing on (0, 2) A) I and II B) L II, and III C)LII, and ? D) L II and IV E) all of these 6x +8 4) 24x+ 10 22x C)--za- 10 2x -1 A) B) D) (2x-1)2 (2x 1)2 (2x -1)2Explanation / Answer
1) We have given The cost C of a system as a function of processor speed C=6s^2-5s+1400
when cost is minimum C'=0
differentiating C with respect to s
C'=12s-5=0
s=5/12=0.41666666666
s=0.4 MHz
2) We have given total cost to produce x units of perfume is C(x)=(3x+9)(6x+6)
Average Cost is C(x)/x=[(3x+9)(6x+6)]/x=[18x^2+18x+54x+54]/x=[18x^2+72x+54]/x=18x+72+54/x
Average Cost is C(x)/x=18x+72+54/x
the marginal average cost is (C(x)/x)'=18+0-54/x^2=18-54/x^2
the marginal average cost is (C(x)/x)'=18-54/x^2
3) We have given f(x)=x^4-x^3
f'(x)=4x^3-3x^2
f''(x)=12x^2-6x
f''(x)=12x^2-6x=0
x(12x-6)=0 implies x=0,x=1/2
f''(-1)=12(-1)^2-6(-1)=12+6>0
f''(1/4)=12(1/4)^2-6(1/4)=-0.75<0
f''(1)=12(1)^2-6(1)=12>0
the signs changes either sides of the x=0 and x=1/2
so inflection points are x=0,1/2
when x=0,f(0)=0
when x=1/2,f(1/2)=(1/2)^4-(1/2)^3=1/8*(1/2-1)=-1/16
inflection points are (0,0) and (1/2,-1/16)
the function is increasing on the interval (1/2,2) the function is not increasing on (0,2) because f''(1/4)=-0.75<0
so answer is I and II
4) We have given y=(6x+8)/(2x-1)
using quotient rule d(u/v)/dx=[v(du/dx)-u(dv/dx)]/v^2 where u=(6x+8) and v=(2x-1)
dy/dx=[(2x-1)*(6)-(6x+8)*(2)]/(2x-1)^2
=[12x-6-12x-16]/(2x-1)^2
=-22/(2x-1)^2
dy/dx=-22/(2x-1)^2
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