[tex]y =x^{3} -2x^{2} +5 \: \: \: \: \: x \in [-1;1]\\y'=3x^{2} -2*2x+0=3x^{2} -4x=3x(x-1\frac{1}{3} )\\x_{1} =0 \: \: \: \: x_{2} =1\frac{1}{3} \\+++++[0]-----[1\frac{1}{3}]+++++\\x_{max} =0\\x_{min} =1\frac{1}{3} \\\\y(-1)=(-1)^{3} -2*(-1)^{2} +5=-1-2+5=2\\y(0)=0^{3} -2*0^{2} +5=5\\y(1)=1^{3} -2*1^{2} +5=1-2+5=4[/tex]
Ответ: y max = 5 ; y min = 2
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[tex]y =x^{3} -2x^{2} +5 \: \: \: \: \: x \in [-1;1]\\y'=3x^{2} -2*2x+0=3x^{2} -4x=3x(x-1\frac{1}{3} )\\x_{1} =0 \: \: \: \: x_{2} =1\frac{1}{3} \\+++++[0]-----[1\frac{1}{3}]+++++\\x_{max} =0\\x_{min} =1\frac{1}{3} \\\\y(-1)=(-1)^{3} -2*(-1)^{2} +5=-1-2+5=2\\y(0)=0^{3} -2*0^{2} +5=5\\y(1)=1^{3} -2*1^{2} +5=1-2+5=4[/tex]
Ответ: y max = 5 ; y min = 2