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
2. Intro to Derivatives
Basic Graphing of the Derivative
Problem 55b
Textbook Question
A capacitor is a device in an electrical circuit that stores charge. In one particular circuit, the charge on the capacitor Q varies in time as shown in the figure. <IMAGE>
b. Is Q′ positive or negative for t≥0?
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1
Step 1: Understand the problem context. The problem involves a capacitor in an electrical circuit where the charge Q on the capacitor varies over time. We need to determine the sign of the derivative of Q, denoted as Q', for t ≥ 0.
Step 2: Recall that the derivative Q' represents the rate of change of the charge Q with respect to time t. If Q' is positive, it means the charge is increasing over time. If Q' is negative, it means the charge is decreasing over time.
Step 3: Analyze the behavior of the charge Q over time from the given figure (not provided here). Look for whether the charge is increasing or decreasing as time progresses for t ≥ 0.
Step 4: If the graph of Q versus t shows an upward trend for t ≥ 0, then Q' is positive. Conversely, if the graph shows a downward trend, then Q' is negative.
Step 5: Conclude based on the observed trend in the graph. If the graph is flat (neither increasing nor decreasing), then Q' would be zero.
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