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

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 ke^(px) then (k)/(p) has the value equal to

f(x)={-x^(2),quad f or x =0 Find x intercept of tangent to f(x) at x=0

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

If f(x)=cos(ln x) then f(x)f(y)-(1)/(2)(f((x)/(y))+f(xy)) has the value