Compute the slope of f(x):
[tex]f(x)=\frac{20}{x^2}[/tex]
For x = -2
[tex]f(-2)=\frac{20}{(-2)^2}=\frac{20}{4}=5[/tex]
Find the line with slope m = 5 and passing through (-2,5):
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-5=5(x-(-2)) \\ y-5=5(x+2) \\ y-5=5x+10 \\ y-5+5=5x+10+5 \\ y=5x+15 \end{gathered}[/tex]
Answer: equation of the tangent line is y = 5x + 15
