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Question

Find the local maxima and minima of the function y=x33x+2.

A
6 , 3
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B
4 , 0
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C
8 , 4
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D
0 , 4
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Solution

The correct option is B 4 , 0
Given function y=x33x+2
dydx=3x23.......(1)
At stationary points, dydx=0,
3x23=0
3(x21)=0
(x1)(x+1)=0
x=1,x=1

Differentiating the equation on both sides again,
d2ydx2=6x .....(2)
Putting x=1 in equation (2)
d2ydx2=6>0
At point x=1 , local minimum occurs
and local minimum is given by
y(1)=(1)33(1)+2=0
Now, putting x=1 in equation (2)
d2ydx2=6<0
So, at point x=1, local maximum occurs and local maximum is given by y(1)=(1)33(1)+2=4
So, local maximum and minimum are 4 and 0, respectively

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