What is the nature of the function $f(x) = \sin x$ at $x = 2\pi / 3$?

Let $f$ be a function defined on $[a, b]$ such that $f^{\prime}(x) > 0$ for all $x \in (a, b)$. Prove that $f$ is an increasing function on $(a, b)$.

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

The range in which $y = -x^{2} + 6x - 3$ is increasing is

Show that the function given by $f(x) = \sin x$ is neither increasing nor decreasing in $(0, \pi)$.

If $f(x)=e^{x}(x-2)^{2}$,then