If `f(0)=0,f^(prime)(0)=2,` then the derivative of `y=f(f(f(x)))` at `x=0` is 2 (b) 8 (c) 16 (d) 4

If f(0)=0,f'(0)=2 then the derivative of y=f(f(f(x))) at x=0 is

If f(x) is differentiable and strictly increasing function,then the value of lim_(x rarr0)(f(x^(2))-f(x))/(f(x)-f(0)) is 1 (b) 0(c)-1 (d) 2

If A=f(x)=[(cosx, sinx, 0),(-sinx, cosx,0),(0,0,1)], then the value of A^-1= (A) f(x) (B) -f(x) (C) f(-x) (D) -f(-x)

A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot If f^(prime)(0)=1/2,t h e n (a)f^(prime)(x)=f(x)=0 (b)4f^(x)+f(x)=0 (c)f^(x)+f(x)=0 (d)4f^(x)-f(x)=0

Let f:[0,2]->R be a function which is continuous on [0,2] and is differentiable on (0,2) with f(0)=1 L e t :F(x)=int_0^(x^2)f(sqrt(t))dtforx in [0,2]dotIfF^(prime)(x)=f^(prime)(x) . for all x in (0,2), then F(2) equals (a)e^2-1 (b) e^4-1 (c)e-1 (d) e^4

If f(x) is continuous in [0,2] and f(0)=f(2). Then the equation f(x)=f(x+1) has

If f(0) = 0 , f' ( 0 ) = 2 and y = f ( f ( f ( f ( x ) ) ) ) , then y'( 0 ) is equal to

Let f be a continuous,differentiable,and bijective function.If the tangent to y=f(x) at x=a is also the normal to y=f(x) at x=b ,then there exists at least one c in(a,b) such that f'(c)=0 (b) f'(c)>0f'(c)<0 (d) none of these