Наибольшее значение функции будет 3 при x=0
Дискриминант Д=36+140=136
1x=(6+√176)/10 2x=(6-√176)/10
1x=(3+2√11)/5 2x=(3-2√11)/5
периметр=(a+b)×2
(3+2√11)/5+(3-2√11)/5=6 6×2=12cm^2
0,15х-0,6=9,9-0,3х+0,3
0,15х+0,3х=10,2+0,6
0,45х=10,8
х=24
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![f(x)=7x^3+ \frac{2}{x^2}-x^2\cdot \sqrt{x} +3= 7x^3+ 2x^{-2}-x^{ \frac{5}{2} }} +3\\ f'(x)= (7x^3+ 2x^{-2}-x^{ \frac{5}{2} }} +3)'= (7x^3)'+ (2x^{-2})'-(x^{ \frac{5}{2} }})' +(3)'=\\ =21x^2+2\cdot(-2)x^{-3}- \frac{5}{2}x^{ \frac{3}{2} } =21x^2- \frac{4}{x^3} - \frac{5}{2} \sqrt{x^3} =\\ =21x^2- \frac{4}{x^3} - \frac{5}{2} x\sqrt{x}](https://tex.z-dn.net/?f=f%28x%29%3D7x%5E3%2B+%5Cfrac%7B2%7D%7Bx%5E2%7D-x%5E2%5Ccdot+%5Csqrt%7Bx%7D+%2B3%3D+7x%5E3%2B+2x%5E%7B-2%7D-x%5E%7B+%5Cfrac%7B5%7D%7B2%7D+%7D%7D+%2B3%5C%5C%0Af%27%28x%29%3D+%287x%5E3%2B+2x%5E%7B-2%7D-x%5E%7B+%5Cfrac%7B5%7D%7B2%7D+%7D%7D+%2B3%29%27%3D+%287x%5E3%29%27%2B+%282x%5E%7B-2%7D%29%27-%28x%5E%7B+%5Cfrac%7B5%7D%7B2%7D+%7D%7D%29%27+%2B%283%29%27%3D%5C%5C%0A%3D21x%5E2%2B2%5Ccdot%28-2%29x%5E%7B-3%7D-+%5Cfrac%7B5%7D%7B2%7Dx%5E%7B+%5Cfrac%7B3%7D%7B2%7D+%7D+%3D21x%5E2-+%5Cfrac%7B4%7D%7Bx%5E3%7D+-+%5Cfrac%7B5%7D%7B2%7D+%5Csqrt%7Bx%5E3%7D+%3D%5C%5C%0A%3D21x%5E2-+%5Cfrac%7B4%7D%7Bx%5E3%7D+-+%5Cfrac%7B5%7D%7B2%7D+x%5Csqrt%7Bx%7D+)
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![f(x)= \sqrt{x} (3-5x)\\ f'(x)=( \sqrt{x} )'(3-5x)+ \sqrt{x} (3-5x)'= \frac{3-5x}{2 \sqrt{x} } -5 \sqrt{x}](https://tex.z-dn.net/?f=f%28x%29%3D+%5Csqrt%7Bx%7D+%283-5x%29%5C%5C%0Af%27%28x%29%3D%28+%5Csqrt%7Bx%7D+%29%27%283-5x%29%2B+%5Csqrt%7Bx%7D+%283-5x%29%27%3D+%5Cfrac%7B3-5x%7D%7B2+%5Csqrt%7Bx%7D+%7D+-5+%5Csqrt%7Bx%7D+)