Question
Asked Oct 5, 2019
Find the slope of the tangent line to the curve
42 4r 4y = 64
at the point (4, 2).
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Find the slope of the tangent line to the curve 42 4r 4y = 64 at the point (4, 2). Preview Get help: Video

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Step 1

Obtain the derivative of the function with respect to x as follows.

d
-(4х? + 4лу- 4у?) -
-(64)
dx
dx
dy
dy
= 0
8х + 4х +4у-12 у*
d
dк
(4х - 12 у)
-8х - 4у
dx
(8х +4у)
(4х-12у?)
фу
ск
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d -(4х? + 4лу- 4у?) - -(64) dx dx dy dy = 0 8х + 4х +4у-12 у* d dк (4х - 12 у) -8х - 4у dx (8х +4у) (4х-12у?) фу ск

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Step 2

Find the slope of the equation at the point (4, 2) as follows.

(8(4)+4(2))
(4(4)-12(2))
(4,2)
(32+8)
|(16-48)
40
-32
5
4
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(8(4)+4(2)) (4(4)-12(2)) (4,2) (32+8) |(16-48) 40 -32 5 4

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Step 3

The equation of the straight line passes through the point is given by,

yy1 = m...

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