if f(X) is continuous in [a,b] and differentiable in in (a.b) then there exists atleast one c (a,b) such that {f(b)-f(a)}/{b³-a³} is equal to

i)3c²f '(c)  ii)f '(c)/3c²  iii)f(c)f'(c)   iv)f(c)/f '(c)

the answer is f'(c)/3c^2

 

am i rite???

 

see this method

 

multiply and divide by b-a

 

f(b)-f(a)/(b-a)=f'(c)  by legranges mean value theorem!!!!

 

b-a/(b^3-a^3) by our above theorem gives 1/g'(c) where g(x)=x^3 so we get1/ 3c^2

 

so the answer is B ie 2nd option!!!