CUET Mathematics 2026 14th May Shift 2 PYQs

For the function $f(x) = x^x, x > 0$, which of the following are TRUE?

(A) $f'(x) = x^x(1 + \log x)$

(B) $x = e$ is the critical point

(C) $f$ is increasing in $(\frac{1}{e}, \infty)$

(D) $f$ is increasing in $(0, \infty)$

Choose the correct answer from the options given below:

The interval in which the $f(x) = \sin x - \cos x$, $0 \leq x \leq 2\pi$ is strictly decreasing is :

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