The interval in which $f(x)=-2x^3-9x^2-12x+1$ is increasing, is:

For the function $f(x)=ax^3-9ax^2+9x+3, x\in R$, then which of the following statements are True?

(A) $f'(x)=3[ax^2-6ax+3]$

(B) It is increasing for $a\in\left[0,\dfrac{1}{3}\right]\ \forall x\in R$

(C) It is increasing for $a\in(-\infty,0)\ \forall x\in R$

(D) It is increasing for $\forall a\in R$

Choose the correct answer from the options given below:

The minimum value of $f(x) = |2x - 1|$ is

In which of the following interval the function $f(x) = x^x, x > 0$ is strictly increasing?

Consider the function $f(x) = x^4 - 2x^2$, then which of the following are TRUE?

A. $f(x)$ is increasing on $(-1,0)$

B. $f(x)$ is decreasing on $(0,1)$

C. $f(x)$ is increasing on $(-\infty,-1)$

D. $f(x)$ is decreasing on $(1,\infty)$

Choose the correct answer from the options given below:

The function $f(x) = -x^3 + 12x^2 - 36x + 21$ is

A. Increasing on $(-\infty, 2)$

B. Decreasing on $(-\infty, 2)$

C. Increasing on $(2, 6)$

D. Decreasing on $(6, \infty)$

Choose the correct answer from the options given below:

The function $f(x)=17-9x+6x^2-x^3$ is strictly increasing in the interval, is: