If $f(x) = x^3 - 6x^2 + 9x + 3$ is a monotonically decreasing function,then $x$ lies in:

In the interval $(-3,3)$,the function $f(x) = \frac{x}{3} + \frac{3}{x}, x \neq 0$ is :

Let $\lambda^{*}$ be the largest value of $\lambda$ for which the function $f_{\lambda}(x) = 4\lambda x^{3} - 36\lambda x^{2} + 36x + 48$ is increasing for all $x \in \mathbb{R}$. Then $f_{\lambda^{*}}(1) + f_{\lambda^{*}}(-1)$ is equal to:

The interval in which the function $f(x) = \frac{\log(7+x)}{\log(3+x)}$ for $x > 0$ decreases is:

The value of $K$ such that $f(x) = \sin x - \cos x - Kx + 5$ decreases for all positive real values of $x$ is given by

If $f(x)=x^3-10x^2+200x-10$,then