63.9k views
1 vote
Consider a function f(x)=(x²/12)​−2sin(x) with initial guesses x₁​=0 and x₃=4. Find the minimum of the given function using the M-file.

User Baboo
by
8.0k points

1 Answer

6 votes

Final answer:

To find the minimum of the function f(x)=(x²/12)​−2sin(x), write its derivative and use numerical methods in an M-file to find the root of the derivative, which indicates the critical point of the function. Starting from the initial guesses, iterate until you find a minimum within a certain tolerance.

Step-by-step explanation:

To find the minimum of the function f(x)=(x²/12)​−2sin(x) using an M-file, we can use numerical methods like Newton's method or the secant method for finding a root of the derivative of the function, as the root of the derivative indicates where the function might have a minimum (critical point).

First, we need to write the derivative of the function, which is f'(x) = (x/6) - 2cos(x). Then, we would write an M-file in MATLAB that implements the chosen numerical method. The M-file will start from initial guesses x1=0 and x3=4 to calculate subsequent guesses and iterate until it converges to a solution that is within a predefined tolerance.

An example of such an algorithm could involve initializing two values, x1 and x3, computing new points based on the derivative and the previous points until we find a point where the derivative is close to zero. That point is likely to be where the function has a minimum unless it is an inflection point or a maximum, which can be determined by checking the second derivative.

User Wookiekim
by
8.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.