Let f be a real valued differentiable function on `RR` such that f(1)=1. If the y-intercept of the tangent at any point P(x, y) on the curve y=f(x) is equal to four power of abscissa of P, then the value of |f(4)| is equal to.

Let f be a real-valued differentiable function on R (the set of all real numbers) such that f(1)=1. If the y-intercept of the tangent at any point P(x,y) on the curve y=f(x) is equal to the cube of the abscissa of P, then the value of f(-3) is equal to

Let y=f(x) be an invertible function such that x -intercept of the tangent at any point P(x.y) on y=f(x) is equal to the square of abscissa of the point of tangency.If f(2)=1, then f-1((5)/(8))=

The length of tangent at a point P(x_(1),y_(1)) to the curve y=f(x) ,having slope m at P is

If f(x) be a differentiable function such that f(x+y)=f(x)+f(y) and f(1)=2 then f'(2) is equal to

Let f(x) be real valued and differentiable function on R such that f(x+y)=(f(x)+f(y))/(1-f(x)f(y))f(0) is equals a.1 b.0 c.-1 d.none of these

If 2f(x+y)=f(x).f(y) for all real x, y. where f'(0)=3 and f(4)=25 , then the value of f'(4) is equal to