List of top Mathematics Questions on Mean Value Theorem asked in AP EAMCET

If $a^2 x^4 + b^2 y^4 = c^6$, then the maximum value of $xy$ is:
The number of all the values of \( x \) for which the function \[ f(x) = \sin x + \frac{1 - \tan^2 x}{1 + \tan^2 x} \] attains its maximum value on \( [0, 2\pi] \).
If Rolle’s theorem is applicable for the function \( f(x) \) defined by \( f(x) = x^3 + Px - 12 \) on \( [0,1] \), then the value of \( C \) of the Rolle's theorem is:
The value \( c \) of Lagrange’s Mean Value Theorem for \( f(x) = e^x + 24 \) in \( [0,1] \) is:
In each of the following options, a function and an interval are given. Choose the option containing the function and the interval for which Lagrange’s Mean Value Theorem is not applicable.
Mean deviation about the mean for the following data is: \[ \begin{array}{|c|c|} \hline \text{Class Interval} & \text{Frequency} \\ \hline 0-6 & 1 \\ 6-12 & 2 \\ 12-18 & 3 \\ 18-24 & 2 \\ 24-30 & 1 \\ \hline \end{array} \]