In an numerical analysis project I need as an intermediate step to calculate the following: $$\max_{0\leq x\leq3} |f'(x)|,\ \ \max_{0\leq x\leq3} |f''(x)|\ \ \text{and}\ \ \max_{0\leq x\leq3} |f^{(4)}(x)|$$

Where $f(x)=\sin(\cos(\sin(\cos(x^2))))$

I tried using Wolfram Alpha to find the maximum of each function but it says "No global maximum found". I tried using Maxima but I couldn't find the value for those either. Maybe this is because the expression for the derivatives gets very big due to all the nested trig. functions.

How can I numerically find these values? What are some other tools/software that can handle this?

  • $\begingroup$ Try MAPLE (I have 2021.1), it works perfectly: plot(abs(diff(diff(diff(diff(sin(cos(sin(cos(x*x)))), x), x), x), x)), x = 0 .. 3); $\endgroup$ Jan 15 at 9:27
  • $\begingroup$ Not really, I just plotted the functions and tried to estime the maximum values. Do you have a way to solve this? @Moo $\endgroup$ 21 hours ago
  • $\begingroup$ I don't :/ @Moo $\endgroup$ 20 hours ago
  • $\begingroup$ It has built in numerical methods that can find what you are looking for. I am not yet able to find those analytically. $\endgroup$
    – Moo
    19 hours ago

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.