Find the slope of the tangent line using a specific formula

[Centurion1]

Homework Statement

Find the slope of the tangent line using a specific formula

g(x)=3t-t²

at (0,0)

Homework Equations

Im told to use this equation by the book
f(c+deltax) - f(c)
Deltax

The Attempt at a Solution

Everytime i plug it in by way of the books style i get 2c. and then you are supposed to plug in the x value which gives me 0. But the right answer is 3

 

[rochfor1]

Perhaps if you show some of your algebra...

 

[Centurion1]

sorry.

yeah I am not so sure its an aritmetic mistake but a misunderatanding of how to do things. but following what the book said to do here goes,

f(c + deltax) - f(c)
delta x

((c + deltax)² - 3t) - (c² -3t) foil it out
delta x

2c(deltax) + (deltax)² simplify
Delta x

and then my book gets rid of both of the delta x's
i assume by simplyfying and i can only assume the deltax² by plugging in zero because the lim approaches 0


and i get the wrong answer because i end up with 2c (which the book says to do) and then plug in a point which is 0 and its supposed to end up being 3?

 

[rochfor1]

You're getting the wrong answer because f(c + \Delta x) \neq ( c + \Delta x )^2 - 3t. You should think about why.

 

[Centurion1]

thats the problem the book gives an example for linear problems, eg y= x and parabolas, y=x^2

im not sure what to do with this?

 

[rochfor1]

This isn't anything that would be an example in a calculus book, because it's function evaluation. (Although it may be in one of the "introductory" sections.)

If you have a function f(t) what does f(c + \Delta x) mean? It means everywhere in the definition of f that you see a t, you should put a c + \Delta x.

 

[Centurion1]

really? its in chapter two of my calculus book section 2.1 finding the slope for a tangent line.

so your saying it should look like

3(c + Delta x) - (c + Delta x)²

so

3c + 3Delta x - c² + 2c(deltax) + (deltax)²

?

 

[rochfor1]

I know this problem is a calculus problem, I'm saying the issue you're having isn't a calculus issue, so it might not be addressed in the examples.

Yes. You need to put c + \Delta x everywhere you see t. Now do some algebra to simplify...

 

[Centurion1]

oh okay i understand what your saying about what I am doing wrong. i realize that f(x) is meant to plugged in whenever you see x. but the formulas was throwing me off.

but is this over delta x like the equation?

 

[rochfor1]

Yes, the definition of derivative stays the same.

 

[Centurion1]

so you can cancel a single delta x right? what happens with the other delta x's i assume the best one to cancel is the 2c delta x

sorry i know I am making this harder than it should be...