find the smallest value of the surface area A in the vector A and the corresponding values of x and y in the vectors x and y.

>> x = 0.5:0.05:3.5

x =

Columns 1 through 6

0.5000 0.5500 0.6000 0.6500 0.7000 0.7500

Columns 7 through 12

0.8000 0.8500 0.9000 0.9500 1.0000 1.0500

Columns 13 through 18

1.1000 1.1500 1.2000 1.2500 1.3000 1.3500

Columns 19 through 24

1.4000 1.4500 1.5000 1.5500 1.6000 1.6500

Columns 25 through 30

1.7000 1.7500 1.8000 1.8500 1.9000 1.9500

Columns 31 through 36

2.0000 2.0500 2.1000 2.1500 2.2000 2.2500

Columns 37 through 42

2.3000 2.3500 2.4000 2.4500 2.5000 2.5500

Columns 43 through 48

2.6000 2.6500 2.7000 2.7500 2.8000 2.8500

Columns 49 through 54

2.9000 2.9500 3.0000 3.0500 3.1000 3.1500

Columns 55 through 60

3.2000 3.2500 3.3000 3.3500 3.4000 3.4500

Column 61

3.5000

>> y = 1.5./x.^2

y =

Columns 1 through 6

6.0000 4.9587 4.1667 3.5503 3.0612 2.6667

Columns 7 through 12

2.3437 2.0761 1.8519 1.6620 1.5000 1.3605

Columns 13 through 18

1.2397 1.1342 1.0417 0.9600 0.8876 0.8230

Columns 19 through 24

0.7653 0.7134 0.6667 0.6243 0.5859 0.5510

Columns 25 through 30

0.5190 0.4898 0.4630 0.4383 0.4155 0.3945

Columns 31 through 36

0.3750 0.3569 0.3401 0.3245 0.3099 0.2963

Columns 37 through 42

0.2836 0.2716 0.2604 0.2499 0.2400 0.2307

Columns 43 through 48

0.2219 0.2136 0.2058 0.1983 0.1913 0.1847

Columns 49 through 54

0.1784 0.1724 0.1667 0.1612 0.1561 0.1512

Columns 55 through 60

0.1465 0.1420 0.1377 0.1337 0.1298 0.1260

Column 61

0.1224

>> v = x.^2.*y

v =

Columns 1 through 5

1.5000 1.5000 1.5000 1.5000 1.5000

Columns 6 through 10

1.5000 1.5000 1.5000 1.5000 1.5000

Columns 11 through 15

1.5000 1.5000 1.5000 1.5000 1.5000

Columns 16 through 20

1.5000 1.5000 1.5000 1.5000 1.5000

Columns 21 through 25

1.5000 1.5000 1.5000 1.5000 1.5000

Columns 26 through 30

1.5000 1.5000 1.5000 1.5000 1.5000

Columns 31 through 35

1.5000 1.5000 1.5000 1.5000 1.5000

Columns 36 through 40

1.5000 1.5000 1.5000 1.5000 1.5000

Columns 41 through 45

1.5000 1.5000 1.5000 1.5000 1.5000

Columns 46 through 50

1.5000 1.5000 1.5000 1.5000 1.5000

Columns 51 through 55

1.5000 1.5000 1.5000 1.5000 1.5000

Columns 56 through 60

1.5000 1.5000 1.5000 1.5000 1.5000

Column 61

1.5000

>> sa = 4.*(x.*y)+(x).^2

sa =

Columns 1 through 5

12.2500 11.2116 10.3600 9.6533 9.0614

Columns 6 through 10

8.5625 8.1400 7.7813 7.4767 7.2183

Columns 11 through 15

7.0000 6.8168 6.6645 6.5399 6.4400

Columns 16 through 20

6.3625 6.3054 6.2669 6.2457 6.2404

Columns 21 through 25

6.2500 6.2735 6.3100 6.3589 6.4194

Columns 26 through 30

6.4911 6.5733 6.6657 6.7679 6.8794

Columns 31 through 35

7.0000 7.1293 7.2671 7.4132 7.5673

Columns 36 through 40

7.7292 7.8987 8.0757 8.2600 8.4515

Columns 41 through 45

8.6500 8.8554 9.0677 9.2867 9.5122

Columns 46 through 50

9.7443 9.9829 10.2278 10.4790 10.7364

Columns 51 through 55

11.0000 11.2697 11.5455 11.8273 12.1150

Columns 56 through 60

12.4087 12.7082 13.0135 13.3247 13.6416

Column 61

13.9643

>> plot(x,sa,'linestyle',':')

[thiruvarangan punniyaseelan]

sorry its like this idk how to ask questions on this

Answer 1

[ANKUR KUMAR]

You can simply use boolean function to find the location of minimum surface area, and subsquently use the same index to get the values of x and y.

x = 0.5:0.05:3.5;
y = 1.5./x.^2;
sa = 4.*(x.*y)+(x).^2;

index=find(sa==min(sa));

smallest_sa=sa(index)
corresponding_x=x(index)
corresponding_y=y(index)