Question

What is the tangent line of a function?

Answer 1

Tangent line:

• The tangent line of a function $f\left(x\right)$ is a line that touches the graph of the function at only one point.
• The tangent line should be parallel to the graph at the point.
• Equation of tangent is given by $(y-y_0)=f\text{'}\left(x_0\right)(x-x_0)$,where $f\text{'}\left(x_0\right)$is slope at that point.

Hence, tangent line of function is $\mathbf{(}\mathit{y}\mathbf{-}{\mathit{y}}_{\mathbf{0}}\mathbf{)}\mathbf{=}\mathit{f}\mathbf{\text{'}}\mathbf{\left(}{\mathit{x}}_{\mathbf{0}}\mathbf{\right)}\mathbf{(}\mathit{x}\mathbf{-}{\mathit{x}}_{\mathbf{0}}\mathbf{)}$