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y* - 4y2 =x4 -9x221. Find the slopes of the devil's curveat the four indicated points.y4- 4y2 x4-9x2(3,2)(3,2)х-33(3,-2)(-3, 2)The slope of the devil's curve at the point (-3, 2) is(Simplify your answer.)The slope of the devil's curve at the point (-3, -2) is(Simplify your answer.)The slope of the devil's curve at the point (3, 2) is(Simplify your answer.)The slope of the devil's curve at the point (3, - 2) is. (Simplify your answer.)

Question

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y* - 4y2 =x4 -9x2
21. Find the slopes of the devil's curve
at the four indicated points.
y4- 4y2 x4-9x2
(3,2)
(3,2)
х
-3
3
(3,-2)
(-3, 2)
The slope of the devil's curve at the point (-3, 2) is
(Simplify your answer.)
The slope of the devil's curve at the point (-3, -2) is
(Simplify your answer.)
The slope of the devil's curve at the point (3, 2) is
(Simplify your answer.)
The slope of the devil's curve at the point (3, - 2) is
. (Simplify your answer.)
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y* - 4y2 =x4 -9x2 21. Find the slopes of the devil's curve at the four indicated points. y4- 4y2 x4-9x2 (3,2) (3,2) х -3 3 (3,-2) (-3, 2) The slope of the devil's curve at the point (-3, 2) is (Simplify your answer.) The slope of the devil's curve at the point (-3, -2) is (Simplify your answer.) The slope of the devil's curve at the point (3, 2) is (Simplify your answer.) The slope of the devil's curve at the point (3, - 2) is . (Simplify your answer.)

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Step 1

Consider the given function.

y4yx9
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y4yx9

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Step 2

Since, the derivative of the curve gives the slope of the given curve.

So, differentiate the above function with respect to x

d
d
(x -9x)
-4y2
dx
8y 4x3 -18.x
4y
dx
dy 4x18.x
(4y-8y)
dy 4x -18x
d 4y8y
dy 9x-2r3
dx 4y-2y
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d d (x -9x) -4y2 dx 8y 4x3 -18.x 4y dx dy 4x18.x (4y-8y) dy 4x -18x d 4y8y dy 9x-2r3 dx 4y-2y

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Step 3

Now, the slope of the given func...

9(-3)-2(-3)'
4 (2)-2(2)
-27-2(-27)
8-2(8)
dy
d )(-3,2)
dy
(-3,2)
dy
dx )(-32)
-27+54
8-16
27
dy
8
dx )(-3,2)
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9(-3)-2(-3)' 4 (2)-2(2) -27-2(-27) 8-2(8) dy d )(-3,2) dy (-3,2) dy dx )(-32) -27+54 8-16 27 dy 8 dx )(-3,2)

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Tagged in

Math

Calculus

Derivative

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