When x = -3, the line that's tangent to f(x) is shown in the given image. So, in order to find the slope of f(x) at x = -3, we need to find the slope of that line.
The slope of a line is given by the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]Now, notice that the points (-4,-7) and (1,3) belong to the tangent line. Therefore, we can use them to find the slope:
y₂ = 3
y₁ = -7
x₂ = 1
x₁ = -4
So, we have:
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{3-(-7)}{1-(-4)}=\frac{3+7}{1+4}=\frac{10}{5}=2[/tex]Therefore, the slope is 2.
