Let P be a point on the graph of y = x³. The tangent line at P will intersect the graph at the point Q. (a) If P has x-coordinate a, then what is the equation of the tangent line at P: y= x + x x (b) The line in (a) will intersect the curve y = x³ in two places; one of these is P and the other point is: ) Hint: This part involves factoring a cubic in x. In general, this may be difficult. However, in this case since we know point P is an interse (c)The ratio of the slope of the curve at Q to the slope at P is
Let P be a point on the graph of y = x³. The tangent line at P will intersect the graph at the point Q. (a) If P has x-coordinate a, then what is the equation of the tangent line at P: y= x + x x (b) The line in (a) will intersect the curve y = x³ in two places; one of these is P and the other point is: ) Hint: This part involves factoring a cubic in x. In general, this may be difficult. However, in this case since we know point P is an interse (c)The ratio of the slope of the curve at Q to the slope at P is
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section: Chapter Questions
Problem 30RE
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Question
![Let P be a point on the graph of y = x³. The tangent line at P will intersect the graph at the point Q.
(a) If P has x-coordinate a, then what is the equation of the tangent line at P:
y=
x +
x
x
(b) The line in (a) will intersect the curve y = x³ in two places; one of these is P and the other point is:
)
Hint: This part involves factoring a cubic in x. In general, this may be difficult. However, in this case since we know point P is an interse
(c)The ratio of the slope of the curve at Q to the slope at P is](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5fffab3e-2167-4e2d-99bf-d85241211098%2F007c3dab-fcc3-4c8b-9125-79ec74aa8349%2Fsolzi7n_processed.png&w=3840&q=75)
Transcribed Image Text:Let P be a point on the graph of y = x³. The tangent line at P will intersect the graph at the point Q.
(a) If P has x-coordinate a, then what is the equation of the tangent line at P:
y=
x +
x
x
(b) The line in (a) will intersect the curve y = x³ in two places; one of these is P and the other point is:
)
Hint: This part involves factoring a cubic in x. In general, this may be difficult. However, in this case since we know point P is an interse
(c)The ratio of the slope of the curve at Q to the slope at P is
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