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

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SUMMARY

The tangent line at the point x=4 for the curve y=2x is determined by evaluating the derivative, which is dy/dx=2. Since the first derivative is constant, the slope of the tangent line remains 2 across the curve. The equation of the tangent line at x=4 can be expressed as y - 8 = 2(x - 4), resulting in y = 2x. This indicates that the tangent line coincides with the original line y=2x at all points.

PREREQUISITES
  • Understanding of derivatives and their applications
  • Familiarity with linear equations
  • Knowledge of slope-intercept form of a line
  • Basic algebraic manipulation skills
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  • Study the concept of derivatives in calculus
  • Learn how to find tangent lines for non-linear functions
  • Explore the implications of constant derivatives on linear functions
  • Practice solving problems involving slope-intercept form
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Students learning calculus, mathematics educators, and anyone interested in understanding the relationship between derivatives and tangent lines.

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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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The tangent to a line is the line itself.
 
Ohhh I forgot you needed to multipliy the slope by x. Thank you very much
 

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