Maximum of my own function

Question

Piotr Grzybowski 2016-10-16

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/307534-maximum-of-my-own-function

编辑： Marc Jakobi 2016-10-16

采纳的回答： Marc Jakobi

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!

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Piotr Grzybowski 2016-10-16

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 2016-10-16

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

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Answer 1

Marc Jakobi 2016-10-16

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/307534-maximum-of-my-own-function#answer_239237

编辑：Marc Jakobi 2016-10-16

在 MATLAB Online 中打开

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]));