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Find the points on the curve y = 2x33x2 - 12x4 where the tangent line is horizontal.(х, у)(smaller x-value)(х, у) з(larger x-value)

Question
Find the points on the curve y = 2x3
3x2 - 12x
4 where the tangent line is horizontal.
(х, у)
(smaller x-value)
(х, у) з
(larger x-value)
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Find the points on the curve y = 2x3 3x2 - 12x 4 where the tangent line is horizontal. (х, у) (smaller x-value) (х, у) з (larger x-value)

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Step 1

Find the points on the curve where the tangent line is horizontal as follows.

The given curve is y = 2x3+3x2–12x...

d
(2х3 + 3х? - 12х + 4)
y'
— бх* + 6х —12
Equate the derivative equal to zero as follows
бх? + бх -12 %3D0
x2x2 0
(х+ 2)(х -1)-0
x -2 or x 1
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d (2х3 + 3х? - 12х + 4) y' — бх* + 6х —12 Equate the derivative equal to zero as follows бх? + бх -12 %3D0 x2x2 0 (х+ 2)(х -1)-0 x -2 or x 1

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