Maximum of my own function

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!

[Image Analyst]

Like you said, if you don't give a range for x, then the answer is simple: it's infinity. And what is f1'? Does the apostrophe/prime mean that that function is actually the derivative of f1 instead of f1 itself?

[Piotr Grzybowski]

Yes, I forgot about it.

f1' is a derivative of f1. But in fact it doesn't change anything in this case.

Not always it will be infinity, how about f(x) = -x^2 + 4 on range x in [-inf, inf] the maximum is 4.

[Marc Jakobi]

Are you sure you are supposed to find the maximal values and not the extrema?

Answer 1

[Marc Jakobi]

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.