Domanda del libro di testo
Calculate the derivative of the following functions.
y = csc ex
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Ch. 3 - Derivatives
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243
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TOC.tableOfContents
- Ch. 1 - Functions210
- Ch. 2 - Limits371
- Ch. 3 - Derivatives633
- Ch. 4 - Applications of the Derivative412
- Ch. 5 - Integration328
- Ch. 6 - Applications of Integration331
- Ch. 7 - Logarithmic, Exponential Functions, and Hyperbolic Functions177
- Ch. 8 - Integration Techniques394
- Ch. 9 - Differential Equations179
- Ch. 10 - Sequences and Infinite Series339
- Ch. 11 - Power Series218
- Ch.12 - Parametric and Polar Curves215
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243Non è quello che usi tu?Cambia libro di testo
Capitolo 3, Problema 33c
Based on sales data over the past year, the owner of a DVD store devises the demand function D(p) = 40 - 2p, where D(p) is the number of DVDs that can be sold in one day at a price of p dollars.
Find the elasticity function for this demand function.
Guida verificata passo dopo passo1
Step 1: Understand the concept of elasticity. Elasticity of demand measures how the quantity demanded of a good responds to a change in price. It is defined as E(p) = - (p / D(p)) * (dD/dp), where D(p) is the demand function and dD/dp is its derivative.
Step 2: Identify the given demand function. The demand function provided is D(p) = 40 - 2p.
Step 3: Differentiate the demand function with respect to p. Find dD/dp by differentiating D(p) = 40 - 2p. The derivative, dD/dp, is the rate of change of demand with respect to price.
Step 4: Substitute D(p) and dD/dp into the elasticity formula. Use the formula E(p) = - (p / D(p)) * (dD/dp) and substitute the expressions for D(p) and dD/dp.
Step 5: Simplify the expression for E(p). Simplify the expression obtained in Step 4 to get the elasticity function in terms of p.
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Demand Function
A demand function expresses the relationship between the price of a good and the quantity demanded by consumers. In this case, D(p) = 40 - 2p indicates that as the price (p) increases, the quantity of DVDs sold (D) decreases. Understanding this function is crucial for analyzing how price changes affect consumer behavior.
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Properties of Functions
Elasticity of Demand
Elasticity of demand measures how responsive the quantity demanded is to a change in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. This concept helps determine whether demand is elastic (sensitive to price changes) or inelastic (less sensitive), which is essential for pricing strategies.
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Calculating Elasticity
To find the elasticity function for the given demand function, we use the formula E(p) = (D'(p) * p) / D(p), where D'(p) is the derivative of the demand function with respect to price. This calculation provides a function that indicates how elasticity varies with price, allowing the store owner to make informed decisions about pricing and inventory.
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04:46Determining Error and Relative Error Example 1
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