- We intersect the surface z = y² - x² with the plane 3x + y = 0, the result is the curve r(t) = (t, -3t, 8t²). What is the slope of the tangent line to the curve at t = 1? Calculate the slope by using directional derivative of z.

- We intersect the surface z = y² - x² with the plane 3x + y = 0, the result is the curve r(t) = (t, -3t, 8t²). What is the slope of the tangent line to the curve at t = 1? Calculate the slope by using directional derivative of z.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

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Question

3. We intersect the surface z = y² - x² with the plane 3x + y = 0,
the result is the curve r(t) = (t, -3t, 8t²).
What is the slope of the tangent line to the curve at t = 1?
Calculate the slope by using directional derivative of z.

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