Table of contents
- 0. Functions4h 53m
- 1. Limits and Continuity2h 2m
- 2. Intro to Derivatives1h 33m
- 3. Techniques of Differentiation2h 18m
- 4. Derivatives of Exponential & Logarithmic Functions1h 16m
- 5. Applications of Derivatives2h 19m
- 6. Graphical Applications of Derivatives6h 0m
- 7. Antiderivatives & Indefinite Integrals48m
- 8. Definite Integrals4h 36m
- 9. Graphical Applications of Integrals1h 43m
- 10. Integrals of Inverse, Exponential, & Logarithmic Functions21m
- 11. Techniques of Integration2h 7m
- 12. Trigonometric Functions6h 54m
- Angles29m
- Trigonometric Functions on Right Triangles1h 8m
- Solving Right Triangles23m
- Trigonometric Functions on the Unit Circle1h 19m
- Graphs of Sine & Cosine46m
- Graphs of Other Trigonometric Functions32m
- Trigonometric Identities52m
- Derivatives of Trig Functions42m
- Integrals of Basic Trig Functions28m
- Integrals of Other Trig Functions10m
- 13: Intro to Differential Equations2h 23m
- 14. Sequences & Series1h 53m
- 15. Power Series2h 19m
0. Functions
Introduction to Functions
Struggling with Business Calculus?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Which of the following best describes what companies must do to create successful new products, in terms of functions?
A
Reduce the number of product features to minimize costs.
B
Focus solely on increasing production without analyzing market trends.
C
Identify and model the relationship between product features and customer demand using functions.
D
Ignore mathematical models and rely only on intuition.

1
Step 1: Understand the context of the problem. The question is asking about how companies can use mathematical functions to create successful new products. This involves applying Business Calculus concepts to model relationships.
Step 2: Recall that a function in mathematics represents a relationship between two variables. In this case, the variables are 'product features' (independent variable) and 'customer demand' (dependent variable).
Step 3: Companies can use functions to analyze how changes in product features (e.g., quality, price, design) impact customer demand. This helps in making data-driven decisions rather than relying on intuition.
Step 4: By identifying and modeling this relationship, companies can optimize product features to maximize customer satisfaction and profitability. This is a key application of Business Calculus in real-world scenarios.
Step 5: The correct approach is to use mathematical models, such as functions, to analyze and predict customer behavior, rather than ignoring data or focusing solely on cost reduction or production increases.
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