Question

For `f(x)=(2x+1)^2/(x+1/2)` what is the equation of the tangent line at `x=-1`?

Answer 1

The equation of the tangent line at `x=−1` is `f(x)`.

Explanation:

`f(x)=(2x+1)^2/(x+1/2)`
`f(x)=(2 (x+1/2))^2/(x+1/2)`
`f(x)=4 xx (x+1/2)`
`f(x)=4x +2` : this is the equation of a straight line.

`=> f(x)` and the tangent line at `x=−1`are coincident lines.
https://www.desmos.com/calculator/cz7vriwsya