If `f(x)` is a differentiable function satisfying `f^(')(x)lt2` for all `xepsilonR` and `f(1)=2,` then greatest possible integral value of `f(3)` is

If f:RR-> RR is a differentiable function such that f(x) > 2f(x) for all x in RR and f(0)=1, then

If f:RR-> RR is a differentiable function such that f(x) > 2f(x) for all x in RR and f(0)=1, then

Suppose f is a differentiable real function such that f(x)+f^(prime)(x)lt=1 for all x , and f(0)=0, then the largest possible value of f(1) is (1) e^(-2) (2) e^(-1) (3) 1-e^(-1) (4) 1-e^(-2)

If f is a real-valued differentiable function such that f(x) f'(x)lt0 for all real x, then

If f is a real-valued differentiable function such that f(x)f'(x)lt0 for all real x, then -

f(x) is a real valued function, satisfying f(x+y)+f(x-y)=2f(x).f(y) for all yinR , Then

If f is a real- valued differentiable function such that f(x)f'(x) lt 0 for all real x, then

If f(x) is a ploynomial function satisfying f(x) . f(1/x) = f(x) + f(1/x) and f(3)=28, then f(2) is

Let f(x) be a differentiable function in [2, 7] . If f(2) = 3 and f'(x) lt= 5 for all x in (2, 7), then the maximum possible value of f (x) at x=7 is