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The formula given below can be used to find the equation of a tangent line to a curve. (y - y 1) = m(x - x 1) Here m is the slope of the tangent line and (x 1, y 1) is the point on the curve at where the tangent line is drawn.
The equation of the tangent to y=f(x) at the point x=a is given by the formula: y=f'(a)(x-a)+f(a). The formula for the equation of tangent is derived from . The gradient of the tangent when is equal to the derivative at the point , which is given by .
- Equations of Lines
- Equation of Tangent Line
- Normal Line Equation
- Video Tutorial w/ Full Lesson & Detailed Examples
So, what do we remember about equations for lines? Well, they require just two elements: 1. Point 2. Slope
This means that to find the equation of a tangent line to a curve, f(x), we simply need two elements: point and slope. The only difference is that to find our slope (i.e., rate of change), we will use derivatives! Is your mind blown yet?
Likewise, we can even extend this concept to writing equations of normal lines, which are also called perpendicular lines. The only difference will be that we will simply use the negative reciprocal slope of the line tangent.
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Feb 20, 2016 · This calculus video tutorial shows you how to find the equation of a tangent line with derivatives. Techniques include the power rule, product rule, and imp...
- 12 min
- 2M
- The Organic Chemistry Tutor
Sep 25, 2024 · To find the equation of a tangent line, sketch the function and the tangent line, then take the first derivative to find the equation for the slope. Enter the x value of the point you’re investigating into the function, and write the equation in point-slope form.
- 10 min
- 1.3M
- Jake Adams
Feb 23, 2018 · This calculus video tutorial explains how to find the equation of the tangent line with derivatives. It explains how to write the equation of the tangent li...
- 11 min
- 640.8K
- The Organic Chemistry Tutor
People also ask
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To find the equation of a line you need a point and a slope. The slope of the tangent line is the value of the derivative at the point of tangency. The normal line is a line that is perpendicular to the tangent line and passes through the point of tangency.