MATLAB code to find the maximum of a function over an interval

Could someone please help with writing a code to solve the following?

Write a MATLAB code that will find the maximum of the following function over the interval x1 < x < x2 :

f(x) = cos(4x) sin(10x) e^-2x

Find the value of f(x) which corresponds to the maximum over the given interval and print it out

using: fprintf('%.4f',fmax).

For example:

TestResult

x1 = 0.7;

x2 = 0.9;

Result

-0.0611

Answer 1

[Rohit Pappu]

MATLAB doesn't have any functions which can explicit calculate the local maxima. A possible workaround would be to find the minima of -f(x)in the same interval.

Code for calculating maxima

x1 = 0.7;
x2 = 0.9;

[x_max,val] = fminbnd(@(x) -cos(4*x)*sin(10*x)*exp(-2*x),x1,x2);  %%x_max is the maxima of f(x) and val is the value of f(x_max)
val = -val;  %% Negate the value because -f(x) was the function worked upon

Additional documentation can be found here

Answer 2

[Salman Zaheer]

How to get max|| Tx-Sx|| of two functions in interval [-1,1] where Tx= x if x belongs to [-1,0) and Tx= -x if x belongs to [0,1]. Similarly for S any function.