Ex 2.6

1 answer:

5 0

$y=3x^4 -4x^3 -12x^2 +1\\
y'=12x^3-12x^2-24x\\\\
12x^3-12x^2-24x=0\\
12x(x^2-x-2)=0\\
12x(x^2+x-2x-2)=0\\
12x(x(x+1)-2(x+1))=0\\
12x(x-2)(x+1)=0\\
x=0 \vee x=2 \vee x=-1\\\\
\forall{x\in(-\infty,-1)\cup(0,2)}\ y'$
$y(-1)=3\cdot(-1)^4-4\cdot(-1)^3-12\cdot(-1)^2+1=3+4-12+1=-4=\\
=y_{min}$

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