Find the points of local maxima and local minima of the function f given by f(x)=x3−3x+3.
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Solution
f(x)=x3−3x+3
Differentiation w.r.t. x f′(x)=3x2−3+0 ⇒f′(x)=3(x2−1)
Putting f′(x)=0 ⇒3(x2−1)=0 ⇒x2−1=0 ⇒(x−1)(x+1)=0 ⇒x=−1,1
Critical points are x=−1,1
Sign scheme of f′(x):
Finding local maxima and minima for f(x)=x3−3x+3
Local minima: f(1)=13−3(1)+3=1
Local maxima: f(−1)=(−1)3−3(−1)+3=5