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Question

Find the minimum value of a function y, represented as y=x3āˆ’3x2+6.

A
2
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B
0
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C
6
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D
2
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Solution

The correct option is A 2
y=x33x2+6
dydx=3x26x
dydx=0, condition for existence of maxima or minima
3x26x=0x=0,2
d2ydx2=6x6
Checking the double derivative at x=0,2
[d2ydx2]x=0=6,
Hence d2ydx2<0
Maxima exists at x=0
Similarly, [d2ydx2]x=2=6,
Hence, d2ydx2>0
Minima exists at x=2
ymin=233(2)2+6=2

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