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Question -

Show that the tangents to the curve y =7x3 + 11 at the points where x = 2and x = −2 are parallel.



Answer -

The equation of the given curve is y =7x3 + 11.

The slope of the tangent toa curve at (x0y0)is. Therefore, the slope of the tangent at thepoint where x = 2 is given by,

It is observed that the slopes of thetangents at the points where x = 2 and x = −2are equal.

Hence, the two tangents are parallel.

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