How to graph the tangent to a curve at some point?

In summary, the conversation is about using a graphing software to graph three things: the function x^2, its derivative 2x, and the tangent to the curve at point 3. The person wants to know how to input the equation for the tangent line at point 3 into the software. The solution is to use the equation for a tangent line at point (a, f(a)), which is y = f'(a)(x - a) + f(a).
  • #1
Juwane
87
0
Using a graphing software, I'm trying to graph three things:

1. The function [tex]x^2[/tex].
2. It's derivative [tex]2x[/tex].
3. The tangent to the curve at point 3.

Now I know that that if I want to find the slope of the curve at point 3, I should substitute 3 into the derivative [tex]2x[/tex], which will give 6. What I want is the tangent line, not it's slope, at point 3. What equation should I input into the software to show the tangent to the curve at point 3? Please help.
 
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  • #2
Asking the program to get the line tangent to a point on the graph probably depends on the program.
Why not use the equation for a tangent line at point (a, f(a))
y = f'(a)(x - a) + f(a)
 
  • #3
Bohrok said:
Asking the program to get the line tangent to a point on the graph probably depends on the program.
Why not use the equation for a tangent line at point (a, f(a))
y = f'(a)(x - a) + f(a)

It worked! How did you derive this equation?

EDIT: Never mind, I've find out.
 
Last edited:

1. How do I find the slope of the tangent to a curve at a specific point?

In order to find the slope of the tangent at a given point on a curve, you will need to take the derivative of the function at that point. The derivative represents the rate of change of the function at that particular point, also known as the slope of the tangent.

2. What is the formula for the tangent line to a curve at a specific point?

The formula for the tangent line to a curve at a specific point is y = mx + b, where m is the slope of the tangent and b is the y-intercept. To find the slope, take the derivative of the function at the given point and plug it into the formula. To find the y-intercept, substitute the x-value of the given point into the original function and solve for y.

3. Can I use any point on the curve to find the tangent line?

No, in order to find the tangent line to a curve at a specific point, you need to use the derivative of the function at that point. This means that you can only use points that are on the original function, not just any random point on the curve.

4. What is the purpose of graphing the tangent to a curve?

The tangent line to a curve at a given point allows us to analyze the behavior of the curve at that point. It gives us information about the slope and direction of the curve at that point, which can be useful in understanding the overall shape and behavior of the function.

5. Is there a specific method for graphing the tangent to a curve at a specific point?

Yes, there are a few steps you can follow to graph the tangent to a curve at a specific point. First, find the slope of the tangent by taking the derivative of the function at that point. Then, use the slope and the given point to plot the tangent line. Finally, use the tangent line to make observations about the behavior of the curve at that point.

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