List of top Mathematics Questions on Local maxima and minima asked in CBSE CLASS XII

If \( M \) and \( m \) denote the local maximum and local minimum values of the function \( f(x) = x + \frac{1{x} \) (\( x \neq 0 \)) respectively, find the value of \( M - m \).}
If \( x = e^{\cos 3t} \) and \( y = e^{\sin 3t} \), prove that \( \frac{dy}{dx} = -\frac{y \log x}{x \log y} \).