Answered: (a) (1) The graph y = f(x). (b) (2) The… | bartleby

College Algebra

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section1.3: Lines

Problem 3E

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Question

Explain simply by how you did step by step.

(a) (1) The graph y = f(x).
(b) (2) The graph of the inverse y = ƒ¯¹(x).
(c) (2) The line tangent to y = f(x) at x = 3. What is the equation of this line?
(d) (2) The line tangent to y = ƒ¯¹(x) at x = 2. What is the equation of this line?
3
5
y
3
2
1
3
1
+
-5
N
3
4
H

| Let f(x) = √x + 1. Using the space below, create a single sketch including:

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The point P(-12, −9) lies on the curve with equation y = x² + 15x + 27. a) The graph is translated so that the point P is mapped to the point (−12,3). Write down the equation of the transformed function.
a) Select a point on the graph of y = −x² + 2x³ + 13x² − 14x − 24, where the roller coaster is going up and evaluate The First Derivative i. ii. b) Select a point on the graph of y = -x + 2x³ + 13x² − 14x − 24, where the roller coaster is down and evaluate The First derivative The Second Derivative ii. The Second Derivative c) At the highest, or lowest point of the coaster, the first derivative is zero. Does that mean that the second derivative at that point is zero? Explain using correct mathematical language and diagrams/graphs, and examples.
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