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Question

Where does the curve y=x42x2+2 have any horizontal tangents?

A
(0,2),(1,1) and (1,1)
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B
(0,0),(1,1) and (1,3)
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C
(3,4),(2,1) and (1,4)
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D
(0,4),(3,1) and (2,4)
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Solution

The correct option is A (0,2),(1,1) and (1,1)
Calculate dydx (slope of a tangent)
dydx=d(x42x2+2)dx
dydx=4x34x
Solve the equation : dydx=0 (since slope of horizontal tangent is zero)
4x34x=0
4x(x21)=0
x=0,1,1
The curve y=x42x2+2 have horizontal tangents at x=0,1 and 1. The corresponding points on the curve are (0,2),(1,1) and (1,1).

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