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Question

If f(x)=2x33x236x+6 has a local maximum and minimum at x=a and x=b respectively, then ordered pair (a,b) is-

A
(3,2)
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B
(2,3)
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C
(2,3)
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D
(3,2)
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Solution

The correct option is C (2,3)
f(x)
=6x26x36
=6(x2x6)
=0
Hence
x2x6=0
(x3)(x+2)=0
x=3 and x=2
f"(x)
=12x6
Now
f"(3)
=30 Hence minimum.
f"(2)
=30 Hence point of maximum.
a=2,b=3

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