Find an equation of the tangent line to the function y 3x2 at the point P(1, 3). = Soluti

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
icon
Related questions
Question
Find an equation of the tangent line to the function y = 3x2 at the point P(1, 3).
Solution
We will be able to find an equation of the tangent line e as soon as we know its slope m. The difficulty is that we know only one point, P, on e, whereas we need two points
to compute the slope. But observe that we can compute an approximation to m by choosing a nearby point Q(x, 3x²) on the parabola (as in the figure below) and computing
the slope mpo of the secant line PQ. [A secant line, from the Latin word secans, meaning cutting, is a line that cuts (intersects) a curve more than once.]
We choose x # 1 so that Q # P. Then,
3x2 - 3
mpQ =
х- 1
For instance, for the point Q(1.5, 6.75) we have the following.
mpQ
1
.5
The tables below show the values of mpo for several values of x close to 1. The closer Q is to P, the closer x is to 1 and, it appears from the tables, the closer mpo is to
This suggests that the slope of the tangent line e should be m =
Transcribed Image Text:Find an equation of the tangent line to the function y = 3x2 at the point P(1, 3). Solution We will be able to find an equation of the tangent line e as soon as we know its slope m. The difficulty is that we know only one point, P, on e, whereas we need two points to compute the slope. But observe that we can compute an approximation to m by choosing a nearby point Q(x, 3x²) on the parabola (as in the figure below) and computing the slope mpo of the secant line PQ. [A secant line, from the Latin word secans, meaning cutting, is a line that cuts (intersects) a curve more than once.] We choose x # 1 so that Q # P. Then, 3x2 - 3 mpQ = х- 1 For instance, for the point Q(1.5, 6.75) we have the following. mpQ 1 .5 The tables below show the values of mpo for several values of x close to 1. The closer Q is to P, the closer x is to 1 and, it appears from the tables, the closer mpo is to This suggests that the slope of the tangent line e should be m =
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Functions and Change: A Modeling Approach to Coll…
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning