List of top Mathematics Questions on Maxima and Minima asked in MHT CET

The maximum value of the function \( f(x) = -2x^2 + 4x + 1 \) occurs at:

Define \( f(x) = \begin{cases} x^2 + bx + c, & x< 1 \\ x, & x \geq 1 \end{cases} \). If f(x) is differentiable at x=1, then b−c is equal to

The maximum value of $xy$ when $x+2y=8$ is
The function $f(x) = x^3 - 6x^2 + 9x + 2$ has maximum value when $x$ is
The maximum value of the function $f(x) = 3x^3 - 18x^2 + 27x - 40$ on the set $S = \{x \in \mathbb{R} \mid x^2 + 30 \le 11x\}$ is