Question

Find the local maxima and local minima for the given function and also find the local maximum and local minimum values $f\left(x\right)=x^2$

Answer 1

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

Putting this equal to zero, we get

$2x=0$

$\Rightarrow x=0$.

Now let's see the double derivative of this function.

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

Which is constant and always positive. So function will take a minimum value at $x=0$

Value is $f\left(0\right)=0^2=0$

There is no local maxima