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Question

It is given that for the function  f(x) = x3 - 6x2 + ax + b on [1, 3], Rolle's theorem holds with c2+13. If f(1) = f(3) = 0, then a =_______, b =________.


Solution


The given function is f(x) = x3 − 6x2 + ax + b.

It is given that Rolle's theorem holds for f(x) defined on [1, 3] with c=2+13.

f1=f3=0     (Given)

f1=0

1-6+a+b=0

a+b=5        .....(1)

Also,

f3=0

27-54+3a+b=0

3a+b=27     .....(2)

Solving (1) and (2), we get

a = 11 and b = −6

It can be verified that for a = 11 and b = −6, f'2+13=0.

Thus, the values of a and b are 11 and −6, respectively.


It is given that for the function  f(x) = x3 − 6x2 + ax + b on [1, 3], Rolle's theorem holds with c2+13. If f(1) = f(3) = 0, then a = ___11___, b =___−6___.

Mathematics
RD Sharma XII Vol 1 (2019)
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