   Chapter 11.3, Problem 29E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Write the equation of the line tangent to the curve 4 x 2 + 3 y 2 −   4 y −   3   =   0  at  ( − 1 ,   1 ) .

To determine

To calculate: The equation of the tangent line to the curve 4x2+3y24y3=0 at (2,1).

Explanation

Given Information:

The provided equation of the curve is, 4x2+3y24y3=0 and point is (2,1).

Formula used:

The slope of tangent to a curve y=f(x) at point (x,y) is given by the derivative of the curve at that point.

The equation of a line passing through points (x1,y1) and slope m is given by:

yy1=m(xx1)

Calculation:

Consider the provided equation of curve,

4x22y2+3xy3x=26

Now, find the derivative dydx from 4x2+3y24y3=0 by taking the derivative term by term on both sides of the equation as,

d(4x2)dx+ddx(3y2)ddx(4y)ddx(3)=ddx(0)8x6yy<

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