which of the following statements are true?? ( Calculus and Differential equations)(NBHM-$2014$) Which of the following statements are ??

a. Let $\phi$ be a non-negative and continuously differentiable function on $(0,\infty)$ such that $\phi'(x)\le\phi(x)$ for all $x$ $\in (0,\infty)$. Then 

$$lim_{x\to \infty}\phi(x)=0$$ 

b. Let $\phi$ be a non-negative function continuous on $[0,\infty)$ and differentiable on     $(0,\infty)$ such that $\phi(0)=0$ and such that   $\phi'(x)\le\phi(x)$ for all $x$ $\in   (0,\infty)$. Then $\phi=0$.

c. Let $\phi$ be a non-negative function continuous on $[0,\infty)$ and such that 
      $$\phi(x) \le \int_{0}^{x}\phi(t) dt$$ for all $x \in [0,\infty)$. Then $\phi=0$.
Hint(Grownwall's Inequality)
  
  If 
  $$f(t)\leq K+\int_a^tf(s)g(s)ds,$$
  then
  $$f(t)\leq K\exp(\int_a^tg(s)ds)$$
  
  And $K\geq 0$; $f,g$ is nonnegative continuous in $[a,b]$.
All of them are wrong.

For statement 1, consider $\phi(x) = e^x$. For statement 2, consider $\phi(x) = e^x - 1$. For statement 3, consider $\phi(x) = e^x$.