A tangent drawn to the curve $y=f(x)$ at $\mathrm{P}(x, y)$ cuts the X -axis and Y -axis at A and B respectively such that $\mathrm{BP}: \mathrm{AP}=3: 1$, given that $f(1)=1$, then

$f(x)$ is cubic polynomial which has local maximum at $x=-1$. If $f(2)=18, f(1)=-1$ and $f(x)$ has local minima at $x=0$, then

$$ \begin{aligned} & f(x)=\left\{\begin{array}{cc} e^x, & 0 \leq x \leq 1 \\ 2-e^{x-1}, & 1 < x \leq 2 \\ x-e, & 2 < x \leq 3 \end{array} \quad\right. \text { and } \\ & g(x)=\int_0^x f(t) d t, x \in[1,3] \text { then } g(x) \text { has } \end{aligned} $$