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Mathematical Applications for the ...

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

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BuyFindarrow_forward

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 x 2 + y 2 +   2 x 3   =   0  at ( 1 ,   2 ) .

To determine

To calculate: The equation of the tangent line to the curve x2+y2+2x3=0 at (1,2).

Explanation

Given Information:

The provided equation of the curve is, x2+y2+2x3=0 and point is (1,2).

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,

x2+y2+2x3=0

Now, find the derivative dydx from x2+y2+2x3=0 by taking the derivative term by term on both sides of the equation as,

d(x2)dx+ddx(y2)+ddx(2x)ddx(3)=02x+2yy+2=02y

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Chapter 11 Solutions

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