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$The curve y = x^{3} + x^{2} - x has two horizontal tangents. The distance between these two horizontal lines is$

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Correct option is D

Given that f(x)=x3+x2−x=y if the tangents are parallel to x-axis then dydx=0 ⇒3x2+2x-1=0 ⇒ x=−1,x=13 The tangents, at x=−1,x=13are y=1,y=−527∴ Distance between horizontal lines =y1-y2=1+527=3227

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The curve y=x3+x2−x has two horizontal tangents. The distance between these two horizontal lines is

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$The curve y = x^{3} + x^{2} - x has two horizontal tangents. The distance between these two horizontal lines is$