The function $f(x) = x^4 - 4x$ is decreasing in the interval

If $y = 2x + \cot^{-1} x + \log(\sqrt{1 + x^2} - x)$,then $y$

The number of real roots of the equation $x^5+3x^3+4x+30=0$ is

If $f(x) = x \cdot e^{x(1-x)}$,then $f(x)$ is

Let $f: [0, 2] \to R$ be a twice differentiable function such that $f''(x) > 0$ for all $x \in (0, 2)$. If $\phi(x) = f(x) + f(2 - x)$,then $\phi$ is

Let $f$ be any function continuous on $[a, b]$ and twice differentiable on $(a, b)$. If for all $x \in (a, b)$,$f^{\prime}(x) > 0$ and $f^{\prime \prime}(x) < 0$,then for any $c \in (a, b)$,$\frac{f(c)-f(a)}{f(b)-f(c)}$ is greater than