# Finding $\max_{0\leq x\leq3} |f'(x)|$, $\max_{0\leq x\leq3} |f''(x)|$, and $\max_{0\leq x\leq3} |f^{(4)}(x)|$ numerically

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?

• 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); Jan 15 at 9:27
• Not really, I just plotted the functions and tried to estime the maximum values. Do you have a way to solve this? @Moo 21 hours ago
• I don't :/ @Moo 20 hours ago
• It has built in numerical methods that can find what you are looking for. I am not yet able to find those analytically.
– Moo
19 hours ago