If $h(x) = f(x) + f(-x)$,then at the point where $h(x)$ attains an extremum,$f'(x) - f'(-x)$ is equal to:

$A$ wire of length $28 \, m$ is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum?

If $x$ and $y$ are two variables such that $x > 0$ and $xy = 1$,what is the minimum value of $x + y$?

The absolute minimum value of $x^4-x^2-2x+5$ is

Divide $10$ into two parts such that the sum of twice the first part and the square of the second part is minimum. The two parts are:

The area (in sq. units) of the largest rectangle $ABCD$ whose vertices $A$ and $B$ lie on the $x$-axis and vertices $C$ and $D$ lie on the parabola $y = x^{2}-1$ below the $x$-axis,is