List of top Mathematics Questions on Maxima and Minima asked in KEAM

Let \( f(x) = 2x^3 - 9ax^2 + 12a^2x + 1 \), where \( a > 0 \). The minimum of \( f \) is attained at a point \( q \) and the maximum is attained at a point \( p \). If \( p^3 = q \), then \( a \) is equal to:

The minimum value of the function \( \max\{x, x^2\} \) is equal to:

The minimum value of $2x^3 - 9x^2 + 12x + 4$ is:

If \( y = m\log x + nx^2 + x \) has its extreme values at \( x = 2 \) and \( x = 1 \), then \( 2m + 10n = \)

Let \( f(x) = (3\sin^2(10x+11) - 7)^2 \) for \( x \in \mathbb{R} \). Then the maximum value of the function is

The minimum value of \( \sin x + \cos x \) is:

The minimum value of \( \sin x + \cos x \) is:

The minimum value of \( \sin x + \cos x \) is: