Table of contents
- 0. Functions7h 52m
- Introduction to Functions16m
- Piecewise Functions10m
- Properties of Functions9m
- Common Functions1h 8m
- Transformations5m
- Combining Functions27m
- Exponent rules32m
- Exponential Functions28m
- Logarithmic Functions24m
- Properties of Logarithms34m
- Exponential & Logarithmic Equations35m
- Introduction to Trigonometric Functions38m
- Graphs of Trigonometric Functions44m
- Trigonometric Identities47m
- Inverse Trigonometric Functions48m
- 1. Limits and Continuity2h 2m
- 2. Intro to Derivatives1h 33m
- 3. Techniques of Differentiation3h 18m
- 4. Applications of Derivatives2h 38m
- 5. Graphical Applications of Derivatives6h 2m
- 6. Derivatives of Inverse, Exponential, & Logarithmic Functions2h 37m
- 7. Antiderivatives & Indefinite Integrals1h 26m
0. Functions
Properties of Functions
Problem 3.2.45a
Textbook Question
Analyzing slopes Use the points A, B, C, D, and E in the following graphs to answer these questions. <IMAGE>
a. At which points is the slope of the curve negative?
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1
Step 1: Understand that the slope of a curve at a point is determined by the derivative of the function at that point. A negative slope indicates that the function is decreasing at that point.
Step 2: Identify the points on the graph where the curve is sloping downwards as you move from left to right. These are the points where the slope is negative.
Step 3: Examine the graph visually or use the derivative function if available to determine the slope at each point A, B, C, D, and E.
Step 4: For each point, check if the tangent line to the curve at that point has a negative slope. This can be done by observing if the tangent line is angled downwards from left to right.
Step 5: List the points where the slope is negative based on your observations from the graph or calculations from the derivative.
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