Let $f(x) = 4x^3 - 18x^2 + 27x - 5$, $x \in R$. Then which of the following statements are TRUE? (A) $f''(x) = 24x - 36$ (B) f has local maxima at $x = \frac{3}{2}$ but no minima (C) f has neither maxima nor minima (D) f has both maxima and minima Choose the correct answer from the options given below:

Match List-I with List-II

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If maximum value of $f(x) = 2x^3 + 3x^2 - 6ax + 10$ occurs at $x = -3$, then the value of $\alpha$ is ____

Rate of change of area of a circle with respect to radius

(A) When r = 2 cm is $4\pi$ cm²/cm.

(B) When r = 6 cm is $12\pi$ cm²/cm.

(C) When r = 12 cm is $6\pi$ cm²/cm.

(D) When r = 16 cm is $8\pi$ cm²/cm.

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The difference of absoulte maximum (largest) and absoulte minimum (smallest) values of the function $f(x) = 12x^{4/3} - 6x^{1/3}, x \in [-1, 1]$ is

In which of the following intervals, the function $f(x) = -x^2 - 2x + 15$ is decreasing?

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 $-4$

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