show that the function f(x) = x3+x2+x+1 has neither a maximum value nor a minimum value

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We have,f(x)=x3+x2+x+1f'(x)=3x2+2x+1For maximum and minimum value, we must havef'(x)=03x2+2x+1=0x=-2±4-126x=-2±-86 where b2-4ac=4-12=-8 which is negative. So, it has no real roots.So, there is no minimum or maximum value.
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