Question

Find the equation of the tangent line to the function

Answer 1

Compute the slope of f(x):

`f(x)=(20)/(x^2)`

For x = -2

`f(-2)=(20)/((-2)^2)=(20)/(4)=5`

Find the line with slope m = 5 and passing through (-2,5):

`\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}`

Answer: equation of the tangent line is y = 5x + 15