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Ta có:
${f^ / }(x) = a{.3^x}\ln 3.$ Giả thiết ${f^ / }\left( 0 \right) = 2$
$ \Leftrightarrow \,\,\,a\ln 3 = 2\,\,\, \Leftrightarrow \,\,\,a = \frac{2}{{\ln 3}}$
$\int\limits_{1}^2{} {\left( {a{{.3}^x} + b} \right)dx = 12\,\,\, \Leftrightarrow \,\,\left[
{\frac{{a{{.3}^x}}}{{\ln 3}} + bx} \right]} _1^2 = 12\Leftrightarrow \frac{9a}{ln3}+2b-(\frac{3a}{ln3}+b)=12\\\,\,\, \Leftrightarrow b = 12 - \frac{{12}}{{{{\ln }^2}3}}$
ĐS : $a = \frac{2}{{\ln 3}}\,\,,\,\,b = 12 - \frac{{12}}{{{{\ln }^2}3}}$
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