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  1. openstax.org › books › calculus-volume-13.4 Derivatives as Rates of Change - Calculus Volume 1 - OpenStax

    In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velocity in physics, population growth rates in biology, and marginal functions in economics.

  2. www.symbolab.com › openstax-calculus1 › derivatives-as-rates-of-changeStudy Guide - Derivatives as Rates of Change - Symbolab

    Apply rates of change to displacement, velocity, and acceleration of an object moving along a straight line. Predict the future population from the present value and the population growth rate. Use derivatives to calculate marginal cost and revenue in a business situation.

  3. math.libretexts.org › Courses › Highline_College1.3: Rates of Change and Behavior of Graphs

    We want to find the increase in total cost when increasing production from 5000 items to 5001 items. This is equivalent to finding the average rate of change on the interval \([5000, 5001]\). The total cost at 5000 items is: \(TC(5000) = 2000 + 50\sqrt {5000} \approx 5535.53\)

  4. mathful.com › hub › rates-of-changeRates of Change: Key Definitions, Formula & Examples - Mathful

    Rate of change is established as the ratio between modifications among two quantities. Change is observed when a specific quantity either increases or decreases in value. The mechanism to figure the rate of change adopts the formula; Rate of change = (yf - yi) / (xf - xi)

  5. math.libretexts.org › Courses › Angelo_State_University3.4: Rates of Change and Behavior of Graphs

    22 kwi 2021 · Find the average rate of change of a function. Use a graph to determine where a function is increasing, decreasing, or constant. Use a graph to locate local maxima and local minima. Use a graph to locate the absolute maximum and absolute minimum. Gasoline costs have experienced some wild fluctuations over the last several decades.

  6. math.libretexts.org › Bookshelves › Calculus2: Instantaneous Rate of Change- The Derivative

    21 gru 2020 · 2.E: Instantaneous Rate of Change- The Derivative (Exercises) These are homework exercises to accompany David Guichard's "General Calculus" Textmap.

  7. brilliant.org › wiki › instantaneous-rate-of-changeAverage and Instantaneous Rate of Change - Brilliant

    Find the average rate of change of the \(x\)-coordinate of the car with respect to time. Using the formula, we get \[ \text{Rate} = \dfrac{\Delta x}{\Delta t} = \dfrac{14 - 2}{6 - 0} = 2 \text{ m/s}.\ _\square\]

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