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- https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/12%3A_Introduction_to_Calculus/12.05%3A_DerivativesChange divided by time is one example of a rate. The rates of change in the previous examples are each different. In other words, some changed faster than others. If we were to graph the functions, we...Change divided by time is one example of a rate. The rates of change in the previous examples are each different. In other words, some changed faster than others. If we were to graph the functions, we could compare the rates by determining the slopes of the graphs.
- https://math.libretexts.org/Courses/Chabot_College/Chabot_College_College_Algebra_for_BSTEM/03%3A_Functions/3.08%3A_DerivativesChange divided by time is one example of a rate. The rates of change in the previous examples are each different. In other words, some changed faster than others. If we were to graph the functions, we...Change divided by time is one example of a rate. The rates of change in the previous examples are each different. In other words, some changed faster than others. If we were to graph the functions, we could compare the rates by determining the slopes of the graphs.
- https://math.libretexts.org/Workbench/Calculus_I%3A_Differential_Calculus/04%3A_Applications_of_Derivatives/4.01%3A_Related_RatesIf two related quantities are changing over time, the rates at which the quantities change are related. For example, if a balloon is being filled with air, both the radius of the balloon and the volum...If two related quantities are changing over time, the rates at which the quantities change are related. For example, if a balloon is being filled with air, both the radius of the balloon and the volume of the balloon are increasing. In this section, we consider several problems in which two or more related quantities are changing and we study how to determine the relationship between the rates of change of these quantities.
- https://math.libretexts.org/Workbench/Calculus_I%3A_Differential_Calculus/03%3A_Derivatives/3.10%3A_Chapter_3_Review_ExercisesThis page contains exercises on calculus derivatives, including evaluating derivatives, proving statements, and deriving tangent line equations. It emphasizes the interpretation of derivatives in prac...This page contains exercises on calculus derivatives, including evaluating derivatives, proving statements, and deriving tangent line equations. It emphasizes the interpretation of derivatives in practical contexts like water levels and wind speeds. The answer sections illustrate the connection between mathematical calculations and real-world applications by providing derivative functions and their evaluations at specific points.
- https://math.libretexts.org/Courses/Hartnell_College/MATH_25%3A_PreCalculus_(Abramson_OpenStax)/07%3A_Introduction_to_Calculus/7.07%3A_DerivativesChange divided by time is one example of a rate. The rates of change in the previous examples are each different. In other words, some changed faster than others. If we were to graph the functions, we...Change divided by time is one example of a rate. The rates of change in the previous examples are each different. In other words, some changed faster than others. If we were to graph the functions, we could compare the rates by determining the slopes of the graphs.
- https://math.libretexts.org/Workbench/Book-_Precalculus_I_for_Highline_College_w/Rational_Inequalities_and_Equations_of_Circles/1.12%3A_Introduction_to_Calculus/1.12.05%3A_DerivativesChange divided by time is one example of a rate. The rates of change in the previous examples are each different. In other words, some changed faster than others. If we were to graph the functions, we...Change divided by time is one example of a rate. The rates of change in the previous examples are each different. In other words, some changed faster than others. If we were to graph the functions, we could compare the rates by determining the slopes of the graphs.
- https://math.libretexts.org/Courses/Truckee_Meadows_Community_College/TMCC%3A_Precalculus_I_and_II/Under_Construction_test2_12%3A_Introduction_to_Calculus/Under_Construction_test2_12%3A_Introduction_to_Calculus_12.4%3A_DerivativesChange divided by time is one example of a rate. The rates of change in the previous examples are each different. In other words, some changed faster than others. If we were to graph the functions, we...Change divided by time is one example of a rate. The rates of change in the previous examples are each different. In other words, some changed faster than others. If we were to graph the functions, we could compare the rates by determining the slopes of the graphs.
- https://math.libretexts.org/Courses/Queens_College/Preparing_for_Calculus_Bootcamp_(Gangaram)/07%3A_Day_7_(A_Preview_of_Differential_Calculus)/7.04%3A_DerivativesChange divided by time is one example of a rate. The rates of change in the previous examples are each different. In other words, some changed faster than others. If we were to graph the functions, we...Change divided by time is one example of a rate. The rates of change in the previous examples are each different. In other words, some changed faster than others. If we were to graph the functions, we could compare the rates by determining the slopes of the graphs.
- https://math.libretexts.org/Workbench/Calculus_I%3A_Differential_Calculus/03%3A_Derivatives/3.08%3A_Implicit_DifferentiationWe use implicit differentiation to find derivatives of implicitly defined functions (functions defined by equations). By using implicit differentiation, we can find the equation of a tangent line to t...We use implicit differentiation to find derivatives of implicitly defined functions (functions defined by equations). By using implicit differentiation, we can find the equation of a tangent line to the graph of a curve.
- https://math.libretexts.org/Workbench/Calculus_I%3A_Differential_Calculus/04%3A_Applications_of_Derivatives/4.07%3A_LHopitals_RuleIn this section, we examine a powerful tool for evaluating limits. This tool, known as L’Hôpital’s rule, uses derivatives to calculate limits. With this rule, we will be able to evaluate many limits w...In this section, we examine a powerful tool for evaluating limits. This tool, known as L’Hôpital’s rule, uses derivatives to calculate limits. With this rule, we will be able to evaluate many limits we have not yet been able to determine. Instead of relying on numerical evidence to conjecture that a limit exists, we will be able to show definitively that a limit exists and to determine its exact value.
- https://math.libretexts.org/Workbench/Calculus_I%3A_Differential_Calculus/04%3A_Applications_of_Derivatives/4.06%3A_Limits_at_Infinity_and_Asymptotes/4.6E%3A_Exercises_for_Section_4.6This page offers exercises on identifying and evaluating vertical and horizontal asymptotes in mathematical functions and limits. It provides graphs showcasing asymptotic behavior, calculations for de...This page offers exercises on identifying and evaluating vertical and horizontal asymptotes in mathematical functions and limits. It provides graphs showcasing asymptotic behavior, calculations for determining the presence of asymptotes, and evaluations of limits as x approaches extreme values. The text discusses properties of various functions, including local maxima, minima, and inflection points, while outlining conditions for asymptote definitions.
