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a)
$f\left(x\right)=\frac{1}{2}e^x\left(\sin x+\cos x\right)$
$f'\left(x\right)=\frac{1}{2}e^x\left(\cos x-\sin x\right)$

$f'\left(0\right)=\frac{1}{2}\cdot1\cdot\left(1-0\right)=\frac{1}{2}$

$f\left(x\right)=x^3e^x$
$f'\left(x\right)=x^3e^x+3x^2e^x$
$f'\left(x\right)=0$
$x=-3\ tai\ x=0$