Show that the tangents to the curve y = 7x 3 + 11 at the points where x = 2 and x = −2 are parallel.

Question:

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

Updated On: Sep 15, 2023

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

\(\frac{dy}{dx}\)= 21x²

The slope of the tangent to a curve at (x₀, y₀) is \(\frac{dy}{dx}\)]_(x0,y0).

Therefore, the slope of the tangent at the point where x = 2 is given by,

\(\frac{dy}{dx}\)]_x=-2=21(2)²=84

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

Hence, the two tangents are parallel.

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