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Question
Who that the tangents to the curve y = 7x3 + 11 at the points x = 2 and x = −2 are parallel ?
Solution
\[\text { Given: }y = 7 x^3 + 11\]
\[ \therefore \frac{dy}{dx} = 21 x^2 \]
\[\text { Now,} \]
\[\text { Slope of the tangent at } (x = 2) = \left( \frac{dy}{dx} \right)_{x = 2} = 21 \left( 2 \right)^2 = 84\]
\[\text { Slope of the tangent at } (x = - 2) = \left( \frac{dy}{dx} \right)_{x = - 2} = 21 \left( - 2 \right)^2 = 84\]
Both slopes are the same. Hence, the tangents at points x = 2 and x = −2 are parallel.
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