Question

1. use the graph to find n(-1) and n(-1).

Explanation:

Step1: Find \( n(-1) \)

To find \( n(-1) \), we look at the graph of \( y = n(x) \) at \( x = -1 \). From the graph, the point on the curve at \( x = -1 \) has a \( y \)-coordinate of \( -4 \). So, \( n(-1) = -4 \).

Step2: Find \( n'(-1) \)

To find the derivative \( n'(-1) \), we need the slope of the tangent line to the graph of \( n(x) \) at \( x = -1 \). The dashed line appears to be the tangent line at \( x = -1 \). We can use two points on this dashed line to calculate the slope. Let's take two points: when \( x = -5 \), \( y = 0 \) and when \( x = 1 \), \( y = -6 \). The slope \( m \) is given by the formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Plugging in the values, we get \( m=\frac{-6 - 0}{1 - (-5)}=\frac{-6}{6}=-1 \). So, the slope of the tangent line at \( x = -1 \) is \( -1 \), which means \( n'(-1)=-1 \).

Answer:

\( n(-1) = -4 \) and \( n'(-1) = -1 \)