   Chapter 11.3, Problem 46E ### 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 y e x = 2 y + 1  at (0,-1) .

To determine

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

Explanation

Given Information:

The provided equation of the curve is, yex=2y+1 and the point is (0,1).

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,

yex=2y+1

Now, find the derivative dydx from yex=2y+1 by take the derivative term by term on both sides of the equation as,

ddx(yex)=ddx(2y)+ddx(1)yex+exdydx=2dydx

Solve for dydx as,

yex+exdydx=2dydxyex=2dydxexdydx<

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