`y = (1 + 2x)^10, (0, 1)` Find an equation of the tangent line to the curve at the given point.

Textbook Question

Chapter 3, 3.4 - Problem 51 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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Slope of the tangent line to the curve at the given point is equal to the derivative of the function at that point.

`y=(1+2x)^10`

`dy/dx=10(1+2x)^(10-1)*2`

`dy/dx=20(1+2x)^9`

Therefore the slope (m) of the tangent line at (0,1) isĀ 

m= 20(1)^9 = 20

Equation of the tangent line can be found by the point slope form of the line

y-y_1 = m(x-x_1)

y-1=20(x-0)

y-1=20x

y=20x+1

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