The function $f(x)=81-3x^3$ has

For the function, $f(x) = \frac{-3}{4}x^4 - 8x^3 - \frac{45}{2}x^2 - 350$, which of the following statements are correct?

(A) $x = -3$ and $x = -5$ are the only critical points of the given function.

(B) $x = -3$ is a point of local minimum.

(C) The local minimum value at $x = -3$ is 23.1.

(D) $x = -5$ is a point of local maximum.

Choose the correct answer from the options given below:

If the function $f(x) = x^4 - 62x^2 + ax + 9$ has a critical point at $x = 1$, then $a$ is equal to:

The largest open interval in which the function $f(x) = 4x^3 - 5x^2 - 8x + 12$ increases, is:

The rate of change of the area of a circle with respect to its radius $r$, when $r = 3$cm, is:

The function $f(x) = \frac{x}{2} + \frac{2}{x}, x \neq 0$ is increasing on

(A) $(-\infty, -2)$

(B) $(-2, 2)$

(C) $(2, \infty)$

(D) $(-1, 1)$

Choose the correct answer from the options given below:

If the function $f(x) = x^4 - 62x^2 + ax + 9$ attains its local maximum value at $x = 1$, then a is equal to :