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The graph of $y=x^3+a x^2+b x+c$ has no extremum if and only if |
$a^2=b$ $a^2<3 b$ $a^2>2 b$ $a^2>2 b^2$ |
$a^2<3 b$ |
We have, $y=x^3+a x^2+b x+c \Rightarrow \frac{d y}{d x}=3 x^2+2 a x+b$ Clearly, $\frac{d y}{d x}>0$ if $4 a^2-12 b<0$ $\Rightarrow y=f(x)$ will increase continuously if $a^2<3 b$ Hence, $f(x)$ has no extremum iff $a^2<3 b$ |
