Find all the points of local maxima and local minima of the function `f(x)=x^3-6x^2+12 x-8.`

Explanation

At ` x = pi//2, f'(x)` changes sign from + ve to - ve.
y = f(x) has maxima at ` x = pi/2`
At ` x = pi, f'(x)` does not change sign and ` f''(pi) = 0` as the x-axis is tangent to the curve.
` x = pi ` is the point of inflection.
At ` x = 3 pi//2, f''(x)` changes sign from - ve to + ve.
So ` y = 3 pi//2` has minima at ` x = (3pi)/2`.