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

Let $f(x)=x^2+\frac{1}{x^2}$ and $g(x)=x-\frac{1}{x}$ for $x \in R-\{-1,0,1\}$,then the local minimum of $\frac{f(x)}{g(x)}$ is

Let $f(x)$ be a cubic polynomial with $f(1) = -10$,$f(-1) = 6$,and it has a local minima at $x = 1$. Also,$f'(x)$ has a local minima at $x = -1$. Then $f(3)$ is equal to:

The sum of two non-zero numbers is $4$. The minimum value of the sum of their reciprocals is

The number of points in $(-\infty, \infty)$ for which $x^2 - x \sin x - \cos x = 0$ is

The condition that $f(x) = ax^3 + bx^2 + cx + d$ has no extreme value is