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keenneenenene
@keenneenenene
July 2022
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dasdasfa
Y=(x^2-24x+24)*e^(4-x)
y'=(x^2-24x+24)' *e^(4-x) +(e^(4-x) )' *(x^2-24x+24)=(2x-24)e^(4-x) +e^(4-x) *(-1)*(x^2-24x+24)=e^(4-x) *(2x-24-x^2+24x-24)=e^(4-x) *(-x^2 +26x-48);
y'=0; e^(4-x)≠0; -x^2+26x-48=0; x^2-26x+48=0; D/4=169-48=121=11^2;
x1=13-11=2; x2=13+11=24
+ - +
---------------2-------------26---------------->x
макс мин
y'(-1)=1+24+24>0
y'(3)=9-72+24)*e^1<0 Ответ.2
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Answers & Comments
y'=(x^2-24x+24)' *e^(4-x) +(e^(4-x) )' *(x^2-24x+24)=(2x-24)e^(4-x) +e^(4-x) *(-1)*(x^2-24x+24)=e^(4-x) *(2x-24-x^2+24x-24)=e^(4-x) *(-x^2 +26x-48);
y'=0; e^(4-x)≠0; -x^2+26x-48=0; x^2-26x+48=0; D/4=169-48=121=11^2;
x1=13-11=2; x2=13+11=24
+ - +
---------------2-------------26---------------->x
макс мин
y'(-1)=1+24+24>0
y'(3)=9-72+24)*e^1<0 Ответ.2