Let `fa n dg` be differentiable on [0,1] such that `f(0)=2,g(0),f(1)=6a n dg(1)=2.` Show that there exists `c in (0,1)` such that `f^(prime)(c)=2g^(prime)(c)dot`

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(x) and g(x) be differentiable for 0<=x<=1, such that f(0)=0,g(0)=0,f(1)=6. Let there exists real number c in (0,1) such taht f'(c)=2g'(c)* Then the value of g(1) must be 1( b) 3(c)-2(d)-1

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

Let f(x) and g(x) be differentiable for 0<=x<=2 such that f(0)=2,g(0)=1, and f(2)=8. Let there exist a real number c in [0,2] such that f'(c)=3g'(c). Then find the value of g(2)

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(x) and g(x) ar edifferentiable function for 0lex le1 such that f(0)=2,g(0) = 0,f(1)=6,g(1)=2 , then in the interval (0,1)

Let f(x) and g(x) be differentiable for 0<=x<=1 such that f(0)=0 g(0)=6 .let there exists a real number c in (0 1) such that f'(c)=2g'(c) then the value of g(1) must be

Statement 1: If f(x) is differentiable in [0,1] such that f(0)=f(1)=0, then for any lambda in R , there exists c such that f^prime(c)=lambdaf(c),0ltclt1. statement 2: if g(x) is differentiable in [0,1], where g(0) =g(1), then there exists c such that g^prime(c)=0,