MATLAB: Maximum of the own function

functionsmax

Using matlab find maximal values of functions f1 and f2 given by following formulas:
f1'(x) = 5x + 2
f2'(x) = 6x^2 – 3
f1(0) = f2(0) = 100
From my point of view there is of course nothing to use Matlab, both functions f1 and f2 goes to infinity of course but my teacher gave me that exercise.
I tried to solve this with "sym" "symfun" classes, I can count integrals deviratives, but how to get MAX of function on range (-inf, inf)?
Or maybe I've understood exercise bad? Hope for small help, thx for yout time!

Best Answer

syms x
f1 = 5*x + 2;
F1 = int(f1); % integrate
x_ext = solve(f1 == 0); % solve for x = 0
% limits for x --> -inf & inf
m1 = limit(F1, inf); 
m2 = limit(F1, -inf);
% evaluate F1 at extreme point
m3 = subs(F1, x_ext);
% compare results
Maxf1 = max(double([m1; m2; m3]));
f2 = 6*x^2 - 3;
F2 = int(f2);
x_ext = solve(f2 == 0);
m1 = limit(F2, inf);
m2 = limit(F2, -inf);
m3 = subs(F2, x_ext);
Maxf2 = max(double([m1; m2; m3]));
I don't know how F1(100) == F2(100) = 0 would be relevant, though.
Related Question