Water is running into a conical vessel, 18cm deep and 6cm in radius, at the rate of 0.1 $cm^3$/sec. If the water is 4cm deep, then the water level rising at the rate

Let $f(x) = x^3 - 6x^2 + 9x - 8$ be a function, then which of the following statements are TRUE?

(A) $f'(x) = 3(x - 1)(x - 3)$

(B) The critical points of the function are $x = 1$ and $x = 3$

(C) $x = 1$ is the point of local minimum

(D) The local maximum value is $-4$

Choose the correct answer from the options given below:

The interval in which the function $f(x)=x^4-\dfrac{x^3}{3}$ is increasing, is

The maximum value of $f(x)=\dfrac{1}{3(x^2-x+1)}$ is :

For x ∈ ℝ - {0}, the function f(x) = $\frac{3}{x}$ + 7 is decreasing when

Based on above information answer the following question :

If area of the flower bed is maximum, then area (in $m^2$) of the garden, which is outside the flower bed is :

If a revenue function is given by $R(x) = 2027x - 1013x^2 - 675x^3$, then the marginal revenue function (MR) is: