$f(x) = x^2 - 6x + 10$ is an increasing function in the . . . . . . interval.

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

In the interval $\left( -\frac{\pi}{3}, \frac{\pi}{3} \right)$,the function $f(x) = -\frac{x}{2} + \sin x$ is:

Find the intervals in which the function given by $f(x) = \frac{3}{10}x^4 - \frac{4}{5}x^3 - 3x^2 + \frac{36}{5}x + 11$ is $(a)$ increasing $(b)$ decreasing.

In which of the following intervals does $f(x) = \sin x$ increase less rapidly than $g(x) = \cos x$?