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Q.

The constant c of Lagrange’s theorem for f(x)=lx2+mx+n (l≠0) in [a,b] is

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a

a+b2

b

b−a2

c

a−b2

d

a+b3

answer is A.

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Detailed Solution

f1(t)=f(b)−(a)b−a 2lc+m=(lb2+mb+n)−(la2+ma+n)b−a ⇒c=a+b2

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The constant c of Lagrange’s theorem for f(x)=lx2+mx+n (l≠0) in [a,b] is