# Calculus – Find the Derivative at a value of x

By | October 30, 2016

## Find the derivative at a value of x

In this tutorial the students will learn  how to find the derivative of a function at a specific point.  The student will find the point of tangency and the derivative.  Using this information the student will then write the equation of the tangent line.

## Explicit Function

$y=f(x)=\frac {1}{8}x^2-4x+15$

## Derivative

$y'=f'(x)=\frac {1}{4}x-4$

## Slope

$y'=f'(20)=\frac {1}{4}(20)-4=5-4=1$

## Point of Tangency, (20,-15)

$y=f(20)=\frac {1}{8}(20)^2-4(20)+15=-15$

## Tangent Line

$y=x-35$

## Graphing Tool

Click on the link below to see this question on an interactive online graphing calculator