If f(x), g(x) be twice differentiable functions on [0,2] satisfying `f''(x) = g''(x)` ,`f'(1) = 2g'(1) = 4` and `f(2) = 3 g(2) = 9`, then `f(x)-g(x)` at x = 4 equals (A) 0 (B) 10 (C) 8 (D) 2

if f(x) =ax +b and g(x) = cx +d , then f[g(x) ] - g[f(x) ] is equivalent to

If f(x) =x^(2) -2,g (x) =2x+ 1 then f^(@) g (x)

Let f: (-5,5) rarr R be a differentiable function with f(4) = 1, f^(')(4) = 1, f(0) = -1 and f^(')(0) = 1 , If g(x) = f(2f^(2)(x)+2))^(2) , then - g^(')(0) equals

Let f(x)=x^(2) and g(x)=2x+1 be two real functions. Find (f+g) (x), (f-g) (x), (fg) (x), (f/g) (x) .

Let f(x)a n dg(x) be two differentiable functions in Ra n df(2)=8,g(2)=0,f(4)=10 ,a n dg(4)=8. Then prove that g^(prime)(x)=4f^(prime)(x) for at least one x in (2,4)dot

Let x = f(t) and y = g(t), where x and y are twice differentiable function If f^(')(0) = g^(')(0) = f^('')(0) = 2, g^(")(0) = 6 , then the value of ((d^(2)y)/(dx^(2))_(t=0) is equal to

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)=0fora 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