List of practice Questions

Given \(f(x) = 3x^4 + 4x^3 - 12x^2 + 6\), the minimum value of \(f(x)\) is ______.

Find the local maximum point of the function \[ f(x)=-x^3+3x+1 \]

Find the interval where the function \( f(x) = x^2 - 4x + 6 \) is strictly decreasing.

Find the local maximum of \[ f(x)=x^3-3x+2 \]

If \( f(x) = x^5 - 5x^3 + 5x^2 - 1 \), then the number of critical points of \( f(x) \) is:

The function f(x) = x³ - 27x + 4, 1 ≤ x ≤ 6 has

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 \( M - m \).}