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0. Functions(0)

Introduction to Functions
(0)

Piecewise Functions
(0)

Properties of Functions
(0)

Common Functions
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Transformations
(0)

Combining Functions
(0)

Exponent Rules
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Exponential Functions
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Logarithmic Functions
(0)

Properties of Logarithms
(0)

Exponential & Logarithmic Equations
(0)

1. Limits and Continuity(0)

Introduction to Limits
(0)

Finding Limits Algebraically
(0)

Continuity
(0)

2. Intro to Derivatives(0)

Tangent Lines and Derivatives
(0)

Derivatives as Functions
(0)

Basic Graphing of the Derivative
(0)

Differentiability
(0)

3. Techniques of Differentiation(0)

Basic Rules of Differentiation
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Higher Order Derivatives
(0)

Product and Quotient Rules
(0)

The Chain Rule
(0)

4. Derivatives of Exponential & Logarithmic Functions(0)

Derivatives of Exponential & Logarithmic Functions
(0)

5. Applications of Derivatives(0)

Implicit Differentiation
(0)

Logarithmic Differentiation
(0)

Related Rates
(0)

Differentials
(0)

Linearization
(0)

6. Graphical Applications of Derivatives(0)

Intro to Extrema
(0)

The First Derivative Test
(0)

Concavity
(0)

The Second Derivative Test
(0)

Curve Sketching
(0)

Finding Global Extrema
(0)

Applied Optimization
(0)

7. Antiderivatives & Indefinite Integrals(0)

Antiderivatives
(0)

Indefinite Integrals
(0)

8. Definite Integrals(0)

Estimating Area with Finite Sums
(0)

Riemann Sums
(0)

Introduction to Definite Integrals
(0)

Fundamental Theorem of Calculus
(0)

Average Value of a Function
(0)

Substitution for Indefinite Integrals
(0)

Substitution for Definite Integrals
(0)

9. Graphical Applications of Integrals(0)

Area Between Curves
(0)

Introduction to Volume & Disk Method
(0)

10. Integrals of Inverse, Exponential, & Logarithmic Functions(0)

Integrals of Exponential Functions
(0)

Integrals Involving Logarithmic Functions
(0)

11. Techniques of Integration(0)

Integration by Parts
(0)

Improper Integrals
(0)

12. Trigonometric Functions(0)

Angles
(0)

Trigonometric Functions on Right Triangles
(0)

Solving Right Triangles
(0)

Trigonometric Functions on the Unit Circle
(0)

Graphs of Sine & Cosine
(0)

Graphs of Other Trigonometric Functions
(0)

Trigonometric Identities
(0)

Derivatives of Trig Functions
(0)

Integrals of Basic Trig Functions
(0)

Integrals of Other Trig Functions
(0)

13: Intro to Differential Equations(0)

Basics of Differential Equations
(0)

Slope Fields
(0)

Separable Differential Equations
(0)

14. Sequences & Series(0)

Sequences
(0)

Review of Factorials
(0)

Series
(0)

15. Power Series(0)

Power Series & Taylor Series
(0)

16. Probability & Calculus(0)

Continuous Probability Models
(0)

2. Intro to Derivatives

Tangent Lines and Derivatives

2. Intro to Derivatives

Tangent Lines and Derivatives: Videos & Practice Problems

Video Lessons Practice Worksheet

Back to all problems

97 of 0

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Problem 97Multiple Choice

During a fireworks display, the concentration of smoke particles $S$ (in $µ {g/m}^{3}$ ) in the air changes over time $t$ (in $minutes$ ). The accompanying figure shows how the smoke concentration changes over time.

During what time intervals is the smoke concentration increasing? What does this indicate about the derivative during those times?

The smoke concentration is increasing from $t equals 0$ to $t equals 20$ $minutes$ , and the derivative is negative during this interval.

The smoke concentration is increasing from $t equals 0$ to $t equals 20$ $minutes$ , and the derivative is positive during this interval.

The smoke concentration is increasing from $t equals 20$ to $t equals 40$ $minutes$ , and the derivative is positive during this interval.

The smoke concentration is increasing from $t equals 20$ to $t equals 40$ $minutes$ , and the derivative is negative during this interval.

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