You are aware that the MATLAB commands max, min find the maximum and minimum elements in an array (and their locations) while fminbnd helps to find the minimum value of a function defined in a function M-file. Seeing there is no such command as fmaxbnd, how can we print out the maximum value of a function f(x), for a ≤ x ≤ b, without using the zoom on facility? For example, find the x and y coordinates of the maximum turning point of y = xe^−x cos x, 0 ≤ x ≤ π.

Using MATLAB

The value of x where f(x) has a maximum is the same as the value where −f(x) is a minimum. Hence, set up the function M-file negf.m

function y=negf(x)

y= - x*exp(-x)*cos(x);

and run the following M-file

clear all

[temp1,temp2]=fminbnd(@negf,0,pi);

xmax=temp1, ymax= -temp2 % gives xmax=0.5959, ymax=0.2718

Using “Maple”

Solve for where the derivative is zero and then substitute back into y = f(x). However, be aware that there might be other (real or complex) solutions to the equation df/dx = 0.

clear all

syms x

f=x*exp(-x)*cos(x);

xmax=double(solve(diff(f))) % gives xmax=0.5959

x=xmax;

ymax=eval(f) % gives ymax=0.2718