Tangent line equation to graph of function

Tangent as the graph of a linear function

If $f$ is differentiable at $x_0$ , the tangent line to $y=f(x)$ at $(x_0;f(x_0))$ is $y=f(x_0)+f'(x_0)(x-x_0).$ $f'(x_0)$ is the slope; the line $y=kx+b$ with $k=f'(x_0)$ , $b=f(x_0)-f'(x_0)x_0$ . The normal (perpendicular to the tangent at the same point) when $f'(x_0)\neq0$ has slope $-1/f'(x_0)$ .

If $f'(x_0)=0$ — the tangent is horizontal ( $y=f(x_0)$ )

Content is available with subscription.

Get full access to all courses on the platform for one year with a single payment.

Unlike other platforms that charge per course, here you get everything for one price, and after one year of use there will be no automatic charge for the following year.