Explanation Given: r ( t ) = 〈 6 t , 4 t 2 , 2 t 3 〉 t = − 2 Formula used: a ( t ) = r ( t ) + t r ' ( t ) Calculation: The tangent line has the parametrization at given point: a ( t ) = r ( t ) + t r ' ( t ) ⇒ a ( t ) = r ( − 2 ) + t r ' ( − 2 ) r ( t ) = 〈 6 t , 4 t 2 , 2 t 3 〉 Given, t = − 2 ⇒ r ( − 2 ) = 〈 6 × ( − 2 ) , 4 × ( − 2 ) 2 , 2 × ( − 2 ) 3 〉 = 〈 − 12 , 16 , − 16 〉 ⇒ r ' ( t ) = 〈 6 , 8 t , 6 t 2 〉 Given, t = − 2 ⇒ r ' ( − 2 ) = 〈 6 , 8 × ( − 2 ) ,<

4th Edition

ISBN: 9781319309671

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 13.2, Problem 34E

To determine

Find a parametrization of the tangent line, r(t)=〈6t,4t2,2t3〉 at the point t=−2.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.2, Problem 33E

Chapter 13.2, Problem 35E

Students have asked these similar questions

The parametric equation of the tangent line to the curve associated to f(t) = (3t², ¾/7,t + 3) at t = −3 is r(t) = Write your answer as a vector valued function.

Let r(t) = (-3t5 - 1, 2e³, 4 sin(4t)) Find the unit tangent vector T(t) at the point t = 0 T(0) -

Let C be the curve defined by the following system of equations: √x+6y²-2²=0 3y = z

Chapter 13 Solutions

CALCULUS: EARLY TRANS 4TH ED W/ ACCESS

Ch. 13.1 - Prob. 1PQ Ch. 13.1 - Prob. 2PQ Ch. 13.1 - Prob. 3PQ Ch. 13.1 - Prob. 4PQ Ch. 13.1 - Prob. 5PQ Ch. 13.1 - Prob. 6PQ Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Find a parametrization of the tangent line, r ( t ) = 〈 6 t , 4 t 2 , 2 t 3 〉 at the point t = − 2.

Solution Summary: The author calculates the tangent line's parametrization at the point t=-2.

Concept explainers

Videos

Find a parametrization of the tangent line, r(t)=〈6t,4t2,2t3〉 at the point t=−2.

Want to see the full answer?

Chapter 13 Solutions