Let $f(x) = \int \frac{x^2-3x+2}{x^4+1} \, dx$. Then the function decreases in the interval:

If $f''(x) < 0$ for all $x \in (0, 2)$,then the function $H(x) = f(1 - x) + 2f(x/2)$ is:

If $f(x)=x^3+a x^2+b x+5 \sin ^2 x$ is an increasing function on $R$,then

For a real number $a$,if a real-valued function $f(x) = 4x^3 + ax^2 + 3x - 2$ is monotonic in its domain,then the range of $a$ is

For what value of $a$ is the function $f(x) = (a + 2)x^3 - 3ax^2 + 9ax - 1$ a decreasing function for all $x \in R$?

Assertion $(A)$: The function $f(x) = x - \log \left(\frac{1+x}{x}\right), x > 0$ has no maximum. Reason $(R)$: If a function $f(x)$ is strictly increasing in an interval $(a, b)$,then at any point in $(a, b)$,$f^{\prime}(x) \neq 0$. The correct option among the following is