Question

verify rolles theorem
f(x)=log[x^2+ab/(a+b)x]​

Answer 1

Answer:

we have

f(x) =log (x^2 + ab )

--------------

(x (a+b)

log (x^2 + ab) - log ( x ( a+ b))

f`(x) = 2x 1

------------ - ------

x^2 + ab x

f`(x) = 2x^2 - x^2 - ab

---------------------

x(x^2 + ab)

x^2 - ab

= -----------

x(x^2 + ab)

Now,

f`(c) = 0 gives c^2 - ab = 0

C= √ab € ( a, b)