Question

For the function $f\left(x\right)=x^2+2x+2$, the point $x=-1$ is a:

• A. Point of Inflection
• B. Maxima
• C. Minima
• D. None of these

Answer 1

The correct option is C Minima

Given,

$f\left(x\right)=x^2+2x+2$

For maxima or minima $f^{\prime }\left(x\right)=0$

$f^{\prime }\left(x\right)=2x+2=0$

$x=-1$

There is one critical point of $f\left(x\right)$

Now for maxima or minima

$f^{\prime \prime }\left(x\right)=2$

$f^{\prime \prime }\left(x\right)=+ve$

Therefore, $(x=-1)$ is a minima to $f\left(x\right)$