Can you prove which is the tangent equation using derivative.
Why the tangent line $l$ through $(x_{0}, f(x_{0}))$ with slope $f'(x_{0})$ is: $l(x)=f(x_{0})+f'(x_{0})(x-x_{0}) \mbox{?}$
Thank!
Can you prove which is the tangent equation using derivative.
Why the tangent line $l$ through $(x_{0}, f(x_{0}))$ with slope $f'(x_{0})$ is: $l(x)=f(x_{0})+f'(x_{0})(x-x_{0}) \mbox{?}$
Thank!
The equation of any line passing through $(x_{0}, f(x_{0}))$ is $\frac{y-f(x_0)}{x-x_0}=m$ where $m$ is the slope.
Now if the line is a tangent of $y=f(x)$ at $(x_{0}, f(x_{0}))$, the slope of the line = the slope of $y=f(x)$ at $(x_{0}, f(x_{0}))$ which is $f'(x_{0})$ .
So, the equation of the line which is a tangent of $y=f(x)$ at $(x_{0}, f(x_{0}))$ will be $\frac{y-f(x_0)}{x-x_0}=f'(x_0)$
Hint : What is the equation of a line through a point with a given slope?