How to graph separate functions from a loop and find their max's?

so i have a function that i need to change one variable a few different times.

I used a for loop and got a few different function outputs, which is what i want.

But i need to plot each one of those functions and find the absolute max on each one as well. I know it will be loops within loops i am just not sure how to call up each individual funtion to graph and then evaluate.

syms t
ymax = 0;
dt = .5;


 for w = 4:dt:7
   x = (4/(-w^2+36))*cos(6*t) + (2/3)*sin(6*t) - (4/(-w^2+36))*cos(w*t)
  
 end
 

these are the functions i get in the command window

 x =
 
cos(6*t)/5 - cos(4*t)/5 + (2*sin(6*t))/3
 
 
x =
 
(16*cos(6*t))/63 - (16*cos((9*t)/2))/63 + (2*sin(6*t))/3
 
 
x =
 
(4*cos(6*t))/11 - (4*cos(5*t))/11 + (2*sin(6*t))/3
 
 
x =
 
(16*cos(6*t))/23 - (16*cos((11*t)/2))/23 + (2*sin(6*t))/3
 
 
x =
 
NaN
 
 
x =
 
(16*cos((13*t)/2))/25 - (16*cos(6*t))/25 + (2*sin(6*t))/3
 
 
x =
 
(4*cos(7*t))/13 - (4*cos(6*t))/13 + (2*sin(6*t))/3
 
>> 

Answer 1

[Aghamarsh Varanasi]

Hi,

You can use the 'fplot' function to plot a function or expression. To calculate the local maxima or local minima of a function, you can refer to this documentation page.

Hope this helps