If f(x) and g(x) are differentiable function for`0lexle1`such that `f(0)=2,g(0)=0,f(1)=6,g(1)=2`, then show that these exist c satisfying `0ltclt1andf'(c)=2g'(c)`

If f(x) and g(x) are differentiable functions for 0lexle1 such that f(0)=2,g(0)=0,f(1)=6,g(1)=2, then in the interval (0,1)

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

If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that f(0)=10 ,g(0)=2,f(1)=2,g(1)=4, then in the interval (0,1)dot (a) f^(prime)(x)=0 for a l lx (b) f^(prime)(x)+4g^(prime)(x)=0 for at least one x (c) f(x)=2g'(x) for at most one x (d) none of these

If f and g are differentiable functions in [0, 1] satisfying f(0)=2=g(1),g(0)=0" and "f(1)=6 , then for some c in [0,1] -

Let f(x)a n dg(x) be differentiable for 0lt=xlt=1, such that f(0)=0,g(0)=0,f(1)=6. Let there exists real number c in (0,1) such taht f^(prime)(c)=2g^(prime)(c)dot Then the value of g(1) must be 1 (b) 3 (c) -2 (d) -1

Let f(x)a n dg(x) be differentiable for 0lt=xlt=2 such that f(0)=2,g(0)=1,a n df(2)=8. Let there exist a real number c in [0,2] such that f^(prime)(c)=3g^(prime)(c)dot Then find the value of g(2)dot

If f(x) and g(x) are twice differentiable functions on (0, 3) satisfying f''(x)=g''(x), f'(1)=4,g'(1)=6,f(2)=3,g(2)=9," then "f(1)-g(1) is -

If f(x) and g(x) are twice differentiable functions on (0,3) satisfying f"(x) = g"(x), f'(1) = 4, g'(1)=6,f(2)=3, g(2) = 9, then f(1)-g(1) is

f(x) and g(x) are two differentiable functions on [0, 2] such that f''(x)-g''(x)=0, f'(1)=2, g'(1)=4, f(2)=3 and g(2)=9 , then [f(x)-g(x)] at x=(3)/(2) is equal to -

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) =lambda f(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,