What is the length of the longest interval in which the function $f(x) = 3\sin x - 4\sin^3 x$ is an increasing function?

If $a < 0$,then the function $f(x) = e^{ax} + e^{-ax}$ is monotonically decreasing for all values of $x$ where ...

For what value of $\lambda$ does the function $f(x) = \lambda x - \sin x$ increase monotonically?

If $f(x) = kx^3 - 9x^2 + 9x + 3$ is monotonically increasing in each interval,then

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

For what values of $a$ is the function $f(x) = x^{2} + ax + 1$ increasing on the interval $[1, 2]$?