Let `y=f(x)` be drawn with `f(0) =2` and for each real number `a` the line tangent to `y = f(x)` at `(a,f(a))` has x-intercept ` (a-2)`. If `f(x)` is of the form of `k e^(px)` then`k/p` has the value equal to

The graph of a certain function fcontains the point (0,2) and has the property that for each number 'p' the line tangent to y=f(x)at(p,f(p)). intersect the x -axis at p+2. Find f(x) .

Given the function f(x)=(a^(x)+a^(-x))/(2)(a>0) If f(x+y)+f(x-y)=kf(x)*f(y) then k has the value 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 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 f(x) be periodic and k be a positive real number such that f(x + k) + f (x) = 0 for all x in R . Then the period of f(x) is

Let f(x) be periodic and k be a positive real number such that f(x+k) + f(x) = 0 for all x in R . Prove that f(x) is periodic with period 2k.

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