Answer
The slope of the curve at $P_1$ is $m_1=1$ and at $P_2$ is $m_2=4$.
Work Step by Step
To estimate the slope $m$ of the curve at point $P(a,b)$ without the equation of the function, we find another point $Q(c, d)$ as near to $P$ as possible in the graph, then the slope of the curve will approximately be equal with the slope of $PQ$: $$m=\frac{d-b}{c-a}$$
1) Find the slope $m_1$ of the curve at $P_1(0,0)$:
In the graph, we see that very near to $P_1$ is a point $Q(0.2,0.2)$.
By calculating the slope of $P_1Q$, we will have the estimated slope $m_1$ of the curve at $P_1$: $$m_1=\frac{0.2-0}{0.2-0}=\frac{0.2}{0.2}=1$$
2) Find the slope $m_2$ of the curve at $P_2(1.1,2)$:
In the graph, we see that very near to $P_2$ is a point $R(1.2,2.4)$.
By calculating the slope of $P_2R$, we will have the estimated slope $m_2$ of the curve at $P_2$: $$m_2=\frac{2.4-2}{1.2-1.1}=\frac{0.4}{0.1}=4$$