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Determine the local maxima and local minima of `f(x)=x^3-6x^2+12x-8` is`

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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`.
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Knowledge Check

  • The total number of local maxima and local minima for the function f(x)=(2+x)^3, -3 less than equal to x less than equal 1, (x^(2//3),-1 less than x less than 2

    A
    0
    B
    1
    C
    2
    D
    3

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