Let `f` be continuous on `[a , b],a >0,a n d` differentiable on `(a , b)dot` Prove that there exists `c in (a , b)` such that `(bf(a)-af(b))/(b-a)=f(c)-cf^(prime)(c)`

If f is continuous on [a,b] and differentiable in (a,b) then there exists c in(a,b) such that (f(b)-f(a))/((1)/(b)-(1)/(a)) is

Tet f be continuous on [a,b] and differentiable on (a,b). If f(a)=a and f(b)=b, then

If f(x) is continuous in [a, b] and differentiable in (a, b), prove that there is atleast one c in (a, b) , such that (f'(c))/(3c^(2))= (f(b)-f(a))/(b^(3)-a^(3)) .

If f(x) is continuous in [a,b] and differentiable in (a,b), then prove that there exists at least one c in(a,b) such that (f'(c))/(3c^(2))=(f(b)-f(a))/(b^(3)-a^(3))

Let f be continuous on [a,b] and differentiable on (a,b). then,which of the following statements is FALSE?

Let f and g be function continuous in [a,b] and differentiable on [a,b] If f(a)=f(b)=0 then show that there is a point c in(a,b) such that g'(c)f(c)+f'(c)=0

If f is a continuous function on [0,1], differentiable in (0, 1) such that f(1)=0, then there exists some c in (0,1) such that cf^(prime)(c)-f(c)=0 cf^(prime)(c)+cf(c)=0 f^(prime)(c)-cf(c)=0 cf^(prime)(c)+f(c)=0