Question

The function $f\left(x\right)=x^2$ has

• A. A maximum value at $x=0$
• B. Minimum value at $x=0$
• C. Finite number of maximum values
• D. Infinite number of maximum values

Answer 1

The correct option is B Minimum value at $x=0$

Given curve is $y=x^2$

$\Rightarrow y^{\prime }=2x$

And $y^{\prime \prime }=2>0$

For max/min of $y$, $y^{\prime }=0$

$\Rightarrow 2x=0\Rightarrow x=0$

Also $y^{\prime \prime }>0$, so $x=0$ is minima of the given curve