Engineering Board Exam Reviewer · Tangent and Normal Lines · medium

Find the points on y=x3-3x+1 where the tangent line is horizontal.

1. (1,-1) and (-1,-3)
2. (1,1) and (-1,3)
3. (1,-1) and (-1,3)
4. (0,1) and (2,3)

Answer

C. (1,-1) and (-1,3)

Solution

y'=3x2-3=0 x= 1. Then y(1)=1-3+1=-1 and y(-1)=-1+3+1=3.

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6. Find the area of the triangle formed by the coordinate axes and the tangent line to y= 1x at x=2.
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