List of top Mathematics Questions on Local maxima and minima

If \( f(x) = x^5 - 5x^3 + 5x^2 - 1 \), then the number of critical points of \( f(x) \) is:
The function \(f(x)= \frac{x^4}{4}-\frac{x^2}{2}\) has
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 \( \frac{dy}{dx} = -\frac{y \log x}{x \log y} \).