37 lines
1.4 KiB
Markdown
37 lines
1.4 KiB
Markdown
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title: Equation of Tangent Line
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---
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## Equation of Tangent Line
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A tangent line to a curve is a straight line that touches a curve, or a graph of a function, at only a single point. The tangent line represents the instantaneous rate of change of the function at that one point. The slope of the tangent line at a point on the function is equal to the derivative of the function at the same point.
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### Finding Equation of the tangent line:
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To find the equation of tangent line to a curve at point x=x0, we need to find the following:
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1. Find the derivative of the function (i.e.derivative of the equation of curve).
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2. Find the value of the derivative by putting x=x0 , this will be the slope of the tangent (say m).
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3. Find the value y0, by putting the value of x0 in the equation of the curve. Our tangent will pass through this point (x0,y0)
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4. Find the equation of the tangent using point-slope form. As the tangent passes through (x0,y0) and have slope m, the equation of the tangent line can be given as:
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(y-y0)=m.(x-x0)
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#### Example : To find the equation of tangent line to the curve f(x) = 4x^2-4x+1 at x=1
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Solution:
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f(x) = 4x^2-4x+1
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Step 1 : f'(x) = 8x-4
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Step 2 : m = f'(2) = 8.2-4 = 12
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Step 3 : y0= f(x0) = f(2) = 4.2^2-4.2+1 = 16-8+1 = 9
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Step 4 : m=12 ; (x0,y0)=(2,9)
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Therefore, equation of tangent line is :
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(y-y0)=m.(x-x0)
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=> (y-9)=12(x-2)
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=> y=12x-15
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