Question

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

• A. has a local minimum
• B. has a local maximum
• C. neither have a local minimum nor local maximum
• D. None of these

Answer 1

Answer: (C)

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