Mercator chart
Classified in Design and Engineering
Written at on 
English with a size of 3.94 KB.
Unit 6: Curve Sketching
Ex 1) Analyze & Sketch f(x) = 2x3-3x2-3x+2
Domain: D={XER} -1| 2, -3, -3, 2
Intercepts: 0=2³-3²-3+2 -2, 5, 2
0=0 (x+1) 2, -5, 2, 0
Y-int: (x+1)(2x²-5x+2)=0
f(0) = 2 (x+1)(x-2)(2x+1)=0
(0,2) X = -1, 2, 1/2
2x2-4x-x-12
int chart =2x(x-2)-(x-2)
=(x-2) (2x-1)
Inc/dec: x=6+-√(-6)2-4(6)(-3)
y'=6x2-6x-3 2(6)
x=6+-√108
Concavity: Y''=12x-6 12
-12x=-6 x=1.4,-0.4
x=0.5 f(1.4)=-2.6 f(-0.4)=2.6
(0.5, 0) (1.4,-2.6) (-0.4,2.6)
min max
Ex 2) Open topped box base twice as long as width. Volume 2400cm3 find dimension minimize amount of cardboard required. (SA)
SA = 2x(x)+2(h)(x)+2(2x)(h)
= 2x² + 2hx + 4xh Dimensions; W=12.16cm, L=24.4cm, H=8.1cm
=2x² + 6hx
=2x² + 6x (1200/x²) 2x(x)h=2400
=2x² + 7200^x-1 2x^2h=2400
SA'=4x-7200x^-2 h=1200/x^2
0=4x-7200x^-2 h=1200/12.16^2
7200/x^2 =4x =8.1cm
7200=4x^3
3√7200 = x
4
12.16 = x