List of top Mathematics Questions on Local maxima and minima

The function \(f(x)=4x^3-18x^2+27x-7\) has:-

If \(f(x)=(x-a)^2+(x-b)^2+(x-c)^2\), then \(f(x)\) has minimum at \(x\) equal to:

The difference between the greatest and least values of the function \(f(x)=\sin 2x-x\) on \(\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\) 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.

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