If `f` be 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

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

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

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

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 a) cf^(prime)(c)-f(c)=0 b) cf^(prime)(c)+cf(c)=0 c) f^(prime)(c)-cf(c)=0 d) cf^(prime)(c)+f(c)=0

Let the set of all function f: [0,1]toR, which are continuous on [0,1] and differentiable on (0,1). Then for every f in S, there exists a c in (0,1) depending on f, such that :

Let the set of all function f: [0,1]toR, which are continuous on [0,1] and differentiable on (0,1). Then for every f in S, there exists a c in (0,1) depending on f, such that :

If f is continuous on [a,b] and differentiable in (a,b) (ab gt 0 ) , then there exists c in (a,b) such that (f(b)-f(a))/((1)/(b) - ( 1)/(a))=

Let f and g be differentiable on [0,1] such that f(0)=2,g(0),f(1)=6 and g(1)=2. Show that there exists c in(0,1) such that f'(c)=2g'(c)

If f is an odd continuous function in [-1,1] and differentiable in (-1,1) then a. f'(A)=f(1)" for some "A in (-1,0) b. f'(B) =f(1)" for some "B in (0,1) c. n(f(A))^(n-1)f'(A)=(f(1))^(n)" for some " A in (-1, 0), n in N d. n(f(B))^(n-1)f'(B)=(f(1))^(n)" for some" B in (0,1), n in N