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Show that the tangents to the curve y = 2x33 at the points where x =2 and x = -2 are parallel.

Solution :

The equation of the curve is y = 2x33

Differentiating with respect to x, we get

dydx = 6x2

Now, m1 = (Slope of the tangent at x = 2) = (dydx)x=2 = 6×(2)2 = 24

and, m2 = (Slope of the tangent at x = -2) = (dydx)x=2 = 6×(2)2 = 24

Clearly m1 = m2.

Thus, the tangents to the given curve at the points where x = 2 and x = -2 are parallel.


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