Using the limit definition to find the derivative of f(x) = x² - 4x

[epatjn]

Homework Statement

Here's the question...use the limit definition to find the derivation of f(x) = x^2-4x

Homework Equations

does this use the definition of the derivative formula (using Larson, et al 4th edition of Precaclulus graphing with limits...and trying to teach someone what to do, but am at a loss at present on what to do...

The Attempt at a Solution

 

[Ray Vickson]

Homework Statement

Here's the question...use the limit definition to find the derivation of f(x) = x^2-4x

Homework Equations

does this use the definition of the derivative formula (using Larson, et al 4th edition of Precaclulus graphing with limits...and trying to teach someone what to do, but am at a loss at present on what to do...

The Attempt at a Solution

I don't have the Larson book, but I assume it defines the derivative (not _derivation_) of f at x to be the limit of the ratio [f(x+h) - f(x)]/h as h --> 0. Well, you can calculate f(x+h) and you know f(x), so you can see what the ratio is equal to. Then you can see what it becomes closer and closer to as h becomes smaller and smaller.

RGV

 

[HallsofIvy]

f(x)= x^2- 4x so f(x+h)= (x+h)^2- 4(x+h)= x^2+ 2hx+ h^2- 4x- 4h

f(x+h)- f(x)= x^2+ 2hx+ h^2- 4x- 4h- (x^2- 4x)= 2hx+ h^2- 4h