Задачи2

[Гост]

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[ammornil]

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[tex]\forall x \in \mathbb{R}: \hspace{0.5em} x^{2} \ge 0 \hspace{0.2em} \Rightarrow \begin{cases} min(x^{2})=0 \\ max(-x^{2})=0 \end{cases}[/tex]

5(a) е решавана тук

[tex]\fbox{\text{5(б)}}\hspace{1em} B=3x^{3}-5x+4-(x^{3}-7x)-(2x^{3}+2x)=\red{3x^{3}}\orange{-5x}+4\red{-x^{3}}\orange{+7x}\red{-2x^{3}}\orange{-2x}=4[/tex]

[tex]\fbox{\text{6}}\hspace{2em}A_{min}=?: A=3y^{4}-(3y^{2}+2y+1)-(3y^{4}-5y^{2}-2y) \\ A=\cancel{\red{3y^{4}}}\orange{-3y^{2}}\cancel{\green{-2y}}-1\cancel{\red{-3y^{4}}}\orange{+5y^{2}}\cancel{\green{+2y}}=2y^{2}-1 \\ \hspace{2em} y^{2}\ge 0, \hspace{0.2em} \forall y \in \mathbb{R} \Rightarrow min(2y^{2})=0 \Rightarrow A_{min}=A(0)=-1[/tex]

[tex]\fbox{\text{7}}\hspace{2em}A_{max}=?: A=9y^{3}-(2y^{3}-3y^{2}+5)+(-7y^{3}-8y^{2}-9) \\ A=\cancel{\red{9y^{3}}}\cancel{\red{-2y^{3}}}\orange{+3y^{2}}-5\cancel{\red{-7y^{3}}}\orange{-8y^{2}}-9=-5y^{2}-14 \\ \hspace{2em} y^{2}\ge 0, \hspace{0.2em} \forall y \in \mathbb{R} \Rightarrow max(-5y^{2})=0 \Rightarrow A_{max}=A(0)=-14[/tex]