   Chapter 11.3, Problem 47E ### 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

# At what points does the curve defined by x 2 + 4 y 2 − 4 x − 4 = 0 have (a) horizontal tangents?(b) vertical tangents?

(a)

To determine

To calculate: The point at which the curve defined by x2+4y24x4=0 has horizontal tangents.

Explanation

Given Information:

The provided equation of the curve is, x2+4y24x4=0.

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 power rule of differentiation:

ddx(xn)=nxn1

Calculation:

Consider the provided equation of curve,

x2+4y24x4=0

Now, find the derivative dydx from x2+4y24x4=0 by taking the derivative term by term on both sides of the equation as,

ddx(x2)+ddx(4y2)ddx(4x)ddx(4)=ddx(0)2x+8ydydx40

(b)

To determine

To calculate: The point at which the curve defined by x2+4y24x4=0 has vertical tangents.

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