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Question

f(x)=x3+ax2+bx+c has a max. at x=1 and min. at x=3. Determine the constants a,b,c.

A
a=3,b=3,c=0.
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B
a=3,b=9,c=3.
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C
a=3,b=9,c=9.
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D
a=3,b=9,c=3.
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Solution

The correct option is B a=3,b=9,c=3.
Given y=x3+ax2+bx+c
dydx=3x2+2ax+b=0

At x=1
32a+b=0
2a+b=3 ....(1)


At x=3
27+6a+b=0

6a+b=27 ....(2)

Solving (1) and (2), we get
a=3,b=9
There is no condition for c, therefore c can assume any real value.
a=3,b=9,cϵR.

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