For $x \in \mathbb{R}$, if $f(x) = -(x-1)^2 + 2$, then (A) $f$ is an increasing function on $(-\infty, 1]$ (B) $f$ has no critical points (C) $f$ has a maximum value at $x = 1$ (D) $f$ has a minimum value at $x = 1$ Choose the correct answer from the options given below:

Match List-I with List-II

Choose the correct answer from the options given below:

The maximum area of a rectangle inscribed in a circle of radius $3\sqrt{2}$ cm, is:

The absolute maximum value of the function $f(x) = 2x^3 - 15x^2 + 36x + 7$ on the interval [1,5] is

If $2x + y = 6$ then the maximum value of $x^2 y$ is :

The height of a closed cylinder of given surface area and maximum volume is equal to the

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