Question

23 и 24
связано с производными

Answer 1

$f(x)= frac{1}{3}sin3x-frac{1}{2}x ; ,; ; f'(x) textless 0\\f'(x)= frac{1}{3}cdot 3cdot cos3x - frac{1}{2} textless 0\\cos3x textless frac{1}{2}\\-frac{pi}{3}+2pi n textless 3x textless frac{pi}{3}+2pi n; ,; ; nin Z\\-frac{pi }{9}+frac{2pi n}{3} textless x textless frac{pi}{9}+frac{2pi n}{3}; ,; nin Z\\Otvet:; ; D:; xin (-frac{pi}{9}+frac{2pi n}{3}; ;; frac{pi}{9}+frac{2pi n}{3}); .$

$2); ; f(x)=Big (sqrt[4]{x}+ frac{2}{sqrt[4]{x}} Big )Big (sqrt[4]{x}- frac{2}{sqrt[4]{x}} Big )=Big (sqrt[4]{x}Big )^2-Big ( frac{2}{sqrt[4]{x}} Big )^2=sqrt{x}-frac{4}{sqrt{x}}\\f'(x)=frac{1}{2sqrt{x}}- frac{-4cdot frac{1}{2sqrt{x}}}{x} =frac{1}{2sqrt{x}}+frac{2}{xsqrt{x}}\\Otvet:; ; C; .$