If y=x^3+x^2+x+1, then y - Vidyadip

MCQ

If $y=x^3+x^2+x+1$, then $y$

A
has a local minimum
B
has a local maximum
✓
neither have a local minimum nor local maximum
D
None of these

✓

Answer

Correct option: C.

neither have a local minimum nor local maximum

(c) : Let $f(x)=y=x^3+x^2+x+1$
Then, $f^{\prime}(x)=3 x^2+2 x+1$.
For a maximum or minimum, we have
$
f^{\prime}(x)=0 \Rightarrow 3 x^2+2 x+1=0
$
But, this equation gives imaginary values of $x$.
So, $f^{\prime}(x) \neq 0$ for any real value of $x$.
Hence, $f(x)$ does not have a maximum or minimum.

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