   Chapter 2.R, Problem 54E

Chapter
Section
Textbook Problem

# Find the points on the ellipse x 2 + 2 y 2 = 1 where the tangent line has slope 1.

To determine

To find:

Pointonthe ellipse x2+2y2=1 where the tangent line has slope 1.

Explanation

1) Formula:

i. Sum rule:

ddxfx+gx=ddxfx+ddxg(x)

ii. ddxsinx=cosx

iii. ddxcosx=-sinx

iv. Equation of tangent line to the curve y=f(x) at point (a,f(a)) is, (y-f(a))=f(a)(x-a)

2) Given:

x2+2y2=1

Slope=1

3) Calculation:

Differentiate given equation of curve with respect to x,

ddx(x2+2y2)=ddx1

By using sum rule, constant function rule and power rule,

2x+4y.dydx=0

Solving for dy/dx

dydx=-x2y

The slope of tangent at a given point is value of derivative at that point.

But here slope is given as 1, so setting dy/dx equal to 1 we have

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