# Find the slope of the tangent line using a specific formula

• Centurion1
In summary, the slope of the tangent line using a specific formula is 3t-t2. The equation for the slope is found in chapter two of a calculus book, and is f(c+deltax) - f(c). Plugging in the x value for the equation gives you 0. However, when you try to plug in the correct value for deltax, you end up with 2c. You are getting the wrong answer because f(c+\Delta x) \neq ( c+\Delta x )^2 - 3t. The problem isn't with the calculus, it's a misunderstanding of how to do things. However, following what the book said to do here goes, you
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

Perhaps if you show some of your algebra...

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?

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

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?

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 $$c + \Delta x$$.

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

?

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...

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?

Yes, the definition of derivative stays the same.

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...

## 1. What is the formula for finding the slope of a tangent line?

The formula for finding the slope of a tangent line is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the tangent line.

## 2. How do I use the formula to find the slope of a tangent line?

To use the formula, you need to first identify two points on the tangent line. Plug the x and y values of these points into the formula and solve for the slope (m).

## 3. Can the formula be used to find the slope of a tangent line at any point on a curve?

Yes, the formula can be used to find the slope of a tangent line at any point on a curve, as long as you have the coordinates of two points on the tangent line at that point.

## 4. Is there an alternative way to find the slope of a tangent line?

Yes, there is another method called the derivative that can also be used to find the slope of a tangent line at a specific point on a curve.

## 5. Why is finding the slope of a tangent line important in calculus?

Finding the slope of a tangent line is important in calculus because it allows us to determine the instantaneous rate of change of a function at a specific point. This has many applications in fields such as physics and economics.

• Calculus and Beyond Homework Help
Replies
2
Views
898
• Calculus and Beyond Homework Help
Replies
11
Views
1K
• Calculus and Beyond Homework Help
Replies
5
Views
1K
• Calculus and Beyond Homework Help
Replies
13
Views
4K
• Calculus and Beyond Homework Help
Replies
11
Views
4K
• Calculus and Beyond Homework Help
Replies
15
Views
2K
• Calculus and Beyond Homework Help
Replies
9
Views
1K
• Calculus and Beyond Homework Help
Replies
4
Views
515
• Calculus and Beyond Homework Help
Replies
1
Views
959
• Calculus and Beyond Homework Help
Replies
2
Views
2K