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 $(6, \infty)$

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The points on the ellipse $4x^2 + y^2 = 4$ that are farthest from the point (1,0) are;

The function $f(x)=\cot^{-1}x+x$ increases in the interval:

Let height and radius of a right circular cylinder are $h$ and $r$ respectively. If it is open at the top, having a given surface area and greatest volume, then

Match List-I with List-II

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Based on above information answer the following question :

The area of the flower bed $(A(x))$ is given by :

If $f(x) = x^4 - \dfrac{2x^3}{3}$, then $f(x)$ is

A. increasing in $\left(\dfrac{1}{2}, \infty\right)$

B. decreasing in $\left(\dfrac{1}{2}, \infty\right)$

C. increasing in $(-\infty, 0)$

D. decreasing in $(-\infty, 0) \cup \left(0, \dfrac{1}{2}\right)$

Choose the correct answer from the options given below: