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Prove that the following functions do not have maxima or minima: $ (iii)\: h (x) =x^3+x^2+x+1 $

This is third part of multipart q4

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  • $\large\frac{d}{dx}$$\big(x^n\big)=nx^{n-1}$
We have $f(x)=x^3+x^2+x+1$
Differentiating with respect to x
Now $f'(x)=0$
$\Rightarrow 3x^2+2x+1=0$
To find the zeroes of the function, let us apply the quadratic formula,
$\Rightarrow x=\large\frac{-2\pm\sqrt{4-12}}{6}=\frac{-1\pm \sqrt{-2}}{3}$
(i.e) $f'(x)=0$ at imaginary points.
i.e $f(x)\neq 0$ for any real value of $x$.
Hence there is neither maximum nor minimum.


answered Aug 7, 2013 by sreemathi.v
edited Aug 19, 2013 by vijayalakshmi_ramakrishnans

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