Answer
The slope of the curve at $P_1$ is $m_1=-2$.
The slope of the curve at $P_2$ is $m_2=0$.
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 $P_1(-1.4,-1.4)$.
In the graph, we see that very near to $P_1$ is a point $Q(-1.6,-1)$.
By calculating the slope of $P_1Q$, we will have the estimated slope $m_1$ of the curve at $P_1$: $$m_1=\frac{-1-(-1.4)}{-1.6-(-1.4)}=\frac{-1+1.4}{-1.6+1.4}=\frac{0.4}{-0.2}=-2$$
2) Find the slope $m_2$ of the curve at $P_2(1.1,2)$:
In the graph, we see that $P_2$ stands at the very top of a curve in the graph. The tangent line to the curve passing $P_2$ would be parallel with the $x$-axis.
This means that slope of that tangent line is $0$. Thus the slope $m_2=0$.
