CUET Mathematics 2026 19th May Shift 1 PYQs

The points of local maxima and local minima of the $f(x) = x^3 - 6x^2 + 9x + 27$ are

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 function $f(x) = \frac{x}{3} + \frac{3}{x}$ is increasing in the interval: