Toán Làm hộ mình với ạ Y=-3X²+4X-8 trên [0;1] Y=X³+3X²-9X-7 trên [-4;0] 18/09/2021 By Liliana Làm hộ mình với ạ Y=-3X²+4X-8 trên [0;1] Y=X³+3X²-9X-7 trên [-4;0]
Đáp án: \(\eqalign{ & a)\,\,\mathop {\min }\limits_{\left[ {0;1} \right]} y = – 8;\,\,\mathop {\max }\limits_{\left[ {0;1} \right]} y = – {{20} \over 3} \cr & b)\,\,\mathop {\min }\limits_{\left[ {0;1} \right]} y = – 59;\,\,\mathop {\max }\limits_{\left[ {0;1} \right]} y = – 7 \cr} \) Giải thích các bước giải: \(\eqalign{ & a)\,\,y = – 3{x^2} + 4x – 8 \cr & y’ = – 6x + 4 = 0 \Leftrightarrow x = {2 \over 3} \in \left[ {0;1} \right] \cr & y\left( 0 \right) = – 8;\,\,y\left( 1 \right) = – 7;\,\,y\left( {{2 \over 3}} \right) = – {{20} \over 3} \cr & \Rightarrow \mathop {\min }\limits_{\left[ {0;1} \right]} y = – 8;\,\,\mathop {\max }\limits_{\left[ {0;1} \right]} y = – {{20} \over 3} \cr & b)\,\,y = {x^3} + 3{x^2} + 9x – 7 \cr & y’ = 3{x^2} + 6x + 9 > 0\,\,\forall x \cr & \Rightarrow \mathop {\min }\limits_{\left[ {0;1} \right]} y = y\left( { – 4} \right) = – 59;\,\,\mathop {\max }\limits_{\left[ {0;1} \right]} y = y\left( 0 \right) = – 7 \cr} \) Trả lời
Đáp án:
\(\eqalign{
& a)\,\,\mathop {\min }\limits_{\left[ {0;1} \right]} y = – 8;\,\,\mathop {\max }\limits_{\left[ {0;1} \right]} y = – {{20} \over 3} \cr
& b)\,\,\mathop {\min }\limits_{\left[ {0;1} \right]} y = – 59;\,\,\mathop {\max }\limits_{\left[ {0;1} \right]} y = – 7 \cr} \)
Giải thích các bước giải:
\(\eqalign{
& a)\,\,y = – 3{x^2} + 4x – 8 \cr
& y’ = – 6x + 4 = 0 \Leftrightarrow x = {2 \over 3} \in \left[ {0;1} \right] \cr
& y\left( 0 \right) = – 8;\,\,y\left( 1 \right) = – 7;\,\,y\left( {{2 \over 3}} \right) = – {{20} \over 3} \cr
& \Rightarrow \mathop {\min }\limits_{\left[ {0;1} \right]} y = – 8;\,\,\mathop {\max }\limits_{\left[ {0;1} \right]} y = – {{20} \over 3} \cr
& b)\,\,y = {x^3} + 3{x^2} + 9x – 7 \cr
& y’ = 3{x^2} + 6x + 9 > 0\,\,\forall x \cr
& \Rightarrow \mathop {\min }\limits_{\left[ {0;1} \right]} y = y\left( { – 4} \right) = – 59;\,\,\mathop {\max }\limits_{\left[ {0;1} \right]} y = y\left( 0 \right) = – 7 \cr} \)