If `f(x)=(x+3)/(5x^2+x-1)&g(x)=(2x+3x^2)/(20+2x-x^2)` such `f(x)a n dg(x)` are differentiable functions in their domains, then which of the following is/are true f(2)+g(1)=0 (b) f(2) `-` g(1)=0 1f(1)+g(2)=0 (d) f(1)`-` g(2)=0

If f(x)=(x+3)/(5x^2+x-1) and g(x)=(2x+3x^2)/(20+2x-x^2) such that f(x) and g(x) are differentiable functions in their domains, then which of the following is/are true (a) 2f^(prime)(2)+g^(prime)(1)=0 (b) 2f^(prime)(2)-g^(prime)(1)=0 (c) f^(prime)(1)+2g^(prime)(2)=0 (d) f^(prime)(1)-2g^(prime)(2)=0

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

If f(x)a n dg(f) are two differentiable functions and g(x)!=0 , then show trht (f(x))/(g(x)) is also differentiable d/(dx){(f(x))/(g(x))}=(g(x)d/x{f(x)}-g(x)d/x{g(x)})/([g(x)]^2)

Let f(x)={x^2-4x+3,x<3x-4,xgeq3 a n dg(x)={x-3,x<4x^2+2x+2,xgeq4 then which of the following is/are true? (f+g)(3. 5)=0 f(g(3))=3 (fg)(2)=1 (d) (f-g)(4)=0

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)

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), 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

Let f (x) and g (x) be two differentiable functions, defined as: f (x)=x ^(2) +xg'(1)+g'' (2) and g (x)= f (1) x^(2) +x f' (x)+ f''(x). The value of f (1) +g (-1) is:

If f(x), g(x) be twice differentiable function on [0,2] satisfying f''(x)=g''(x) , f'(1)=4 and g'(1)=6, f(2)=3, g(2)=9, then f(x)-g(x) at x=4 equals to:- (a) -16 (b) -10 (c) -8

If f(x)=e^(x)g(x),g(0)=2,g'(0)=1, then f'(0) is