direction Link to heading

  • Create a program that can find the root value or extreme value of a single variable non-linear equation inputted by the user by entering the number of components of the equation in the form of an array.
    • The user cannot input an array with an element that is 0.
    • The maximum number of elements of the array is 5.
    • Use elements of vector (poly2sym, polyder, polyval, inline) for root and extreme value finding procedure.
  • Output is as follow.
    • Choice 1
    Input size of array (max 5): 3
Make sure not to input for any element value of 0
Value of array 1: 1
Value of array 2: 5
Value of array 3: 3

Function = f(x) = x^2 + 5*x + 3

Choose operation to be performed
1. Find one root of the function
2. Find extreme of the function
Your choice: 1

Input your initial guess: 3
Found one root of the function, which is -0.697224
>>
    • Choice 2
    Input size of array (max 5): 3
Make sure not to input for any element value of 0
Value of array 1: 1
Value of array 2: 5
Value of array 3: 3

Function = f(x) = x^2 + 5*x + 3

Choose operation to be performed
1. Find one root of the function
2. Find extreme of the function
Your choice: 2

Input your initial guess: 3
Extreme of the function is -3.25
>>

result of choice 1 Link to heading

>> poly_4_root_extreme
Input size of array (max 5):
3
Value of array 1:
1
Value of array 2:
5
Value of array 3:
3

Function = f(x) = 5*x + x^2 + 3
Choose operation to be performed
1. Find one root of the function
2. Find extreme of the function
Your choice:
1
Your initial guess:
3
Found one root of the function,which is -0.697224

result of choice 2 Link to heading

>> poly_4_root_extreme
Input size of array (max 5):
3
Value of array 1:
1
Value of array 2:
5
Value of array 3:
3

Function = f(x) = 5*x + x^2 + 3
Choose operation to be performed
1. Find one root of the function
2. Find extreme of the function
Your choice:
2
Your initial guess:
3
Extreme of the function is -3.25

code Link to heading

% poly_4_root_extreme

% repeat until n between 1 and 5 
n = 10;
while n > 5 | n < 1 
    n = input('Input size of array (max 5):');
end

% read the coefficents
a = [];
for i = 1:n
    fprintf('Value of array %d:', i);
    c = input('');
    a = [a c];
end
fprintf('\n');

% create and display function
fstr = poly2sym(a);
f = inline(fstr);
fprintf('Function = f(x) = %s\n', fstr);

% Ask operation
fprintf('Choose operation to be performed\n');
fprintf('1. Find one root of the function\n');
fprintf('2. Find extreme of the function\n');
choice = input('Your choice:');

initg = input("Your initial guess:");

if choice == 1
    root = fzero(f, initg);
    fprintf('Found one root of the function,');
    fprintf('which is %.6f', root);
else
    gstr = diff(fstr);
    g = inline(gstr);
    extreme = fzero(g, initg);
    fextreme = f(extreme);
    fprintf('Extreme of the function is ');
    fprintf('%.2f', fextreme);
end