Problem 780 (difficulty: 2/10)

Calculate the extremal values of the following functions on the given interval!

 (1)  \(\displaystyle x^2 -x^4 ; \ [-2,2];\)      (2)  \(\displaystyle x-\arctg x; \ [-1,1];\)      (3)  \(\displaystyle x+e^{-x}; \ [-1,1];\)      (4)  \(\displaystyle x+x^{-2}; \ [1/10, 10];\)      (5)  \(\displaystyle \arctg(1/x); \ [1/10, 10];\)      (6)  \(\displaystyle \cos x^2 ;\ [0,\pi ];\)      (7)  \(\displaystyle \sin (\sin x); \ [-\pi /2,\pi /2];\)      (8)  \(\displaystyle x\cdot e^{-x} ;\ [-2,2];\)      (9)  \(\displaystyle x^n \cdot e^{-x}; \ [-2n,2n];\)      (10)  \(\displaystyle x-\log x; \ [1/2, 2];\)      (11)  \(\displaystyle 1/(1+\sin ^2 x),\ (0,\pi ) ;\)      (12)  \(\displaystyle \sqrt{1-e^{-x^2}}; \ [-2,2];\)      (13)  \(\displaystyle x\cdot \sin (\log x);\ [1,100];\)      (14)  \(\displaystyle x^x;\ (0,\infty );\)      (15)  \(\displaystyle \sqrt[x]{x};\ (0,\infty );\)      (16)  \(\displaystyle (\log x)/x;\ (0,\infty );\)      (17)  \(\displaystyle x\cdot \log x; \ (0,\infty );\)      (18)  \(\displaystyle x^x \cdot (1-x)^{1-x} ; \ (0,1).\)

Give me another random problem!