The function $f(x) = 2x^3 - 9x^2 + 12x + 2$ is decreasing in

Let $p(x)$ be a polynomial with real coefficients, $p(0) = 1$ and $p^{\prime}(x) > 0$ for all $x \in \mathbb{R}$. Then

Let $f(x) = \int {e^x}(x - 1)(x - 2)dx$. Then $f$ decreases in the interval

Let $(2, 3)$ be the largest open interval in which the function $f(x) = 2 \log_e(x-2) - x^2 + ax + 1$ is strictly increasing and $(b, c)$ be the largest open interval in which the function $g(x) = (x-1)^3(x+2-a)^2$ is strictly decreasing. Then $100(a+b-c)$ is equal to:

If $f(x)=x^x$,then the interval in which $f(x)$ decreases is

In the open interval $\left(0, \frac{\pi}{2}\right)$, which of the following is true for the expression $\cos x + x \sin x$?