Condition for Monotonically Decreasing Function

Q. If $f:R\to R$ is a continuous function and satisfies $f\left(x\right)=e^x+\underset{0}{\overset{1}{\int }}{e}^{x}f\left(t\right)dt$, then

1. $f\left(0\right)<0$
2. $f\left(x\right)$ is a decreasing function $\forall x\in R$
3. $f\left(x\right)$ is a increasing function $\forall x\in R$
4. $\underset{0}{\overset{1}{\int }}f\left(x\right)dx>0$

Q.

If f(x) , g(x) and h(x) are three differentiable functions throughout their domains and given that their first derivatives are -

$f^{\prime }\left(x\right)<0$

$g^{\prime }\left(x\right)=0$

$h^{\prime }\left(x\right)\le 0$

throughout their domains. Then choose the correct option of monotonically decreasing functions -

1. Only h(x)

2. f(x) & h(x)

3. g(x) & h(x)

4. f(x), g(x) & h(x)