Show that the tangents to the curve y-7 x3-11 at the points where x-2 and x-2 are parallel-

The equation of the given curve is y = 7x3 + 11. The slope of the tangent to a curve at (x0, y0) is.Therefore, the slope of the tangent at the point where x = ...

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Standard XII

Mathematics

Proof of LaGrange's Mean Value theorem

Show that the...

Question

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

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Solution

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

The slope of the tangent to a curve at (x₀, y₀) is.
Therefore, the slope of the tangent at the point where x = 2 is given by,

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

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