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  4. The values of x at the stationary points of f(x)=x3+3 x2-2 are

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Q. The values of $x$ at the stationary points of $f(x)=x^{3}+3 x^{2}-2$ are

AP EAMCETAP EAMCET 2020

Solution:

Let $y=f(x)=x^{3}+3 x^{2}-2$
$\frac{d y}{d x}=3 x^{2}+6 x$
$\Rightarrow \frac{d^{2} y}{d x^{2}}=6 x+6$
For stationary points $\frac{d y}{d x}=0$
$\Rightarrow 3 x(x+2)=0$
$\Rightarrow x=0,-2$