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Question

Find all points of local maxima and local minima of the function f given by f(x)=x33x+3

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Solution

f(x)=x33x+3

Find all points where f(x)=0

f(x)=3x23=0

x21=0
x=±1

Now check the sign of f′′(x) on these points.
f′′(x)=6x

Now,
f′′(1)=6 which is greater than zero.
So there is local minima at x=1

f′′(1)=6 which is less than zero.
So there is local maxima at x=1



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