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Develop a dynamic graphical representation that illustrates the concept of the time-bound derivative for a function of a variable. Highlight the relationship between the original function and its derivative, emphasizing how the derivative describes the instantaneous rate of change of the function. Use colors and shapes to visualize speed and acceleration, incorporando setas ou curvas que demonstrem claramente o comportamento das grandezas ao longo do tempo. Ensure that the image conveys the idea that the derivative represents the slope of the function at each point, and that this is related to speed and acceleration in a dynamic and continuous context. Seja criativo e assegure que a imagem seja informativa e visualmente atraente para ser usada como capa de uma aula sobre o tema.
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Develop a dynamic graphical representation that illustrates the concept of the time-bound derivative for a function of a variable
.
Highlight the relationship between the original function and its derivative
,
emphasizing how the derivative describes the instantaneous rate of change of the function
.
Use colors and shapes to visualize speed and acceleration
,
incorporando setas ou curvas que demonstrem claramente o comportamento das grandezas ao longo do tempo
.
Ensure that the image conveys the idea that the derivative represents the slope of the function at each point
,
and that this is related to speed and acceleration in a dynamic and continuous context
.
Seja criativo e assegure que a imagem seja informativa e visualmente atraente para ser usada como capa de uma aula sobre o tema
.
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