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Question

If f(x)=x33x2+43 has maximum value a at x=b, then (a,b) is

A
(43,0)
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B
(2,43)
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C
(2,43)
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D
(0,43)
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Solution

The correct option is A (43,0)
Given, f(x)=x33x2+43

f(x)=x22x=0
x=0,2

Now, f′′(x)=2x2
f′′(2)=2>0
and f′′(0)=2<0
f(x) has maximum at x=0 which equals to f(0)=43

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