Let `f` be a continuous function defined onto [0,1] with range [0,1]. Show that there is some `c` in [0,1] such that `f(c)=1-c`

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 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

Leg f be continuous on the interval [0,1] to R such that f(0)=f(1). Prove that there exists a point c in [(0,1)/(2)] such that f(c)=f(c+(1)/(2))

Statement-1: If a continuous funtion on [0,1] satisfy 0 le f(x) le 1 , then there exist c in [0,1] such that f(c )=c Statement-2: lim_(x to c) f(x)=f(c)

Let f(x), be a function which is continuous in closed interval [0,1] and differentiable in open interval 10,1[ Show that EE a point c in]0,1[ such that f'(c)=f(1)-f(0)

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)

Let f be a continuous function satisfying f'(In x)=[1 for 0 1 and f(0)=0 then f(x) can be defined as

The function f(x) is defined in [0,1] . Find the domain of f(tanx).

Let f:[0,1]rarr[0,1] be a continuous function such that f(f(x))=1f or allx in[0,1] then