all papers written from scratch

no plagiarism - GUARANTEED

Free Math Essay Sample

 ← Three Great Reasons to Graduate from College Summative Assesment: Principles and Practice →

Buy Cheap Math Essay

. Differentiate with respect to x

(a)

F(x) =   1/3 x7

F(x) = 1/3x -7

FI(x) = -7/3x-8

fI(x)= -7/3x8

(b)

If f(x) =  g(x)/h(x)

fI(x)= (h(x) gI(x) - g(x)hI(x))/h(x)2

=(x-5) (12x2-4x3) / (x-5)2

= (12x3-60x2-4x3)/ (x2-10x+25)

= (  8x3-60x2) /(x2-10x+25)

(c)

F(x) = (2x2-6)3(3x3-3)

F(x) = g(x)h(x)

fI(x)= g(x) hI(x) + h(x)gI(x)

fI(x) = (2x2-6)2(3x3-3)I+((2x2-6)3)I(3x3-3)

= (2x2-6)2(2x2-6)27x2+((2x2-6)3)I(3x3-3)

=((2x2-6)3)I=U3=3U2=3(2x2-6)2(4x)

= (2x2-6)2(2x2-6)27x2+12x (2x2-6)(3x3-3)

=(4x4-24x2+36)(2x2-6)27x2+12x (4x4-24x2+36)(3x2-3)

=(4x4-24x2+36)(54x4-162x2)+ (48x5-288x3+432x)(3x2-3)

=216x8-1296x8+1944x4-648x8+3888-5832x2 +144x7+864x5+1296x3-144x7+864x5-1296x

fI(x)=-1728x8+1720x5+1944x4+1296x3-5832x2-1296x+3888

(d)

F(x) = xln(2x)

We know dlnU/dx=UI/U

Also F(x)=g(x)h(x)

fI(x)=g(x)hI(x)+h(x)gI(x)

= 2x/2x+ln (2x)

Answers to question 2

TR=P x Q,                           TR- Total Revenue

TR = 400Q - Q2/50

Expression for marginal revenue is,

MR = 400 - Q/25

MR = 400 - 10000 / 25

MR=0

Price elasticity demand when price=100

P = 400 - Q/50

Q/50 = 400 - P

Q=400 x 50 - 50P,

Price elasticity=gradient x P/Q

=-50 x 100/10000

=-1/3 hence inelastic

c) Henry can maximize daily revenue by either increasing the quantity of the commodities. Increase in price may not affect demand for the commodity due to the inelastic demand for the commodity. Increasing the quantity is the only way to maximize profit hence revenue.

a)     A=P(1+R)n

A=P(1+24/1200)12

A=P(1+0.02)12

=P(1.02)12

=1.2682P

I=PRT

R=I/PT = 0.2682P / P=0.2682

=26.82%

b) A=P(1+R)n

A=P(1+R/4)4n

A= P(1+6/400)24

A=12000(1.015)24

A=1.4295 x 12000

=\$17154.03

C) 5/100x 1000x 40 = £ 2000

4. Express the first and the second order derivatives of;

(a)

fI(x,y) = 12x + 5 dy/dx

fII(x,y) = 12 + d2y/dx2

(b) f(x,y) = 3x5y4

fI(x,y)= 15x4y4+3x54y3dy/dx

fII(x,y)= 60x3y4+15x44y3dy/dx+15x4y3dy/dx+3x512y2d2y/dx2

c) f(x,y)=(10+x2y)3

fI(x,y)=U3=3U2.UI

=3(10+x2y)2 (2xy+ x2dy/dx)

Using f(x) =h(x)g(x)

fI(x,y)= h(x)gI(x)+hI(x)g(x),

fI(x,y) = (10+x2y)2(2y+ 2xdy/dx+2xd2y/dx2)+(2xy+x2dy/dx)

fI(x,y)=(300+60x2y+3x4y2)(2xy+x2dy/dx)

=(600xy+120x3y2+6x5y3+300x2dy/dx+60x4ydy/dx+3x6y2dy/dx)

fII(x,y)=600y+600xdy/dx+360x2y2+120x32ydy/dx+30x4y3+6x53y2dy/dx+600xdy/dx+240x3…ydy/dx+60x4d2y/dx2+18x5y2dy/dx+3x62yd2y/dx2.

Related essays   