How can I find the equation of the tangent line at x=4 for y=2x?

In summary, the slope of the tangent line at a point on a curve is found by evaluating the derivative of the curve at that point. For example, if we have the curve y=2x and we want to find the tangent line at x=4, we can use the first derivative dy/dx=2 to determine the slope of the tangent line. However, since the first derivative is a constant, we also need to multiply it by x to find the equation of the tangent line at x=4.
  • #1
fishingspree2
139
0
We know that the slope of the tangent line at a point on a curve is found by evaluating the derivative of the curve at that point.

Say we have the curve y=2x.
Say I wanted to find the tangent line at x=4
dy/dx=2
The first derivative is a constant, which is not surprising since the curve is always changing at the same rate.
However, since the first derivative is a constant, how can I find the equation of the tangent line at x=4? We can't say it's y=2 since that line does not intersect y=2x at x=4.

Can anyone help me
 
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  • #2
The tangent to a line is the line itself.
 
  • #3
Ohhh I forgot you needed to multipliy the slope by x. Thank you very much
 

Related to How can I find the equation of the tangent line at x=4 for y=2x?

1. What is the definition of a tangent line?

A tangent line is a straight line that touches a curve at only one point, without crossing over or intersecting the curve at any other point. It represents the instantaneous rate of change of the curve at that point.

2. How is the slope of a tangent line calculated?

The slope of a tangent line is calculated by finding the derivative of the function at the point of tangency. This can be done using the slope formula (change in y over change in x) or by using the power rule for derivatives.

3. What is the purpose of finding the tangent line?

Finding the tangent line allows us to approximate the behavior of a curve at a specific point. It can also help us determine the maximum or minimum value of a function, as these occur at points where the tangent line is horizontal (slope = 0).

4. Can a line have more than one tangent line?

Yes, a line can have multiple tangent lines if it intersects with a curve at multiple points. Each point of intersection will have its own unique tangent line that represents the instantaneous rate of change at that point.

5. How is the equation of a tangent line determined?

The equation of a tangent line can be determined by using the point-slope form, where the slope is calculated using the derivative of the function at the point of tangency. Alternatively, the equation can also be found by using the slope-intercept form if the point of tangency and slope are known.

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