Exemplo 8 de Precalculus, 12.4 Derivatives

Interpreting a Derivative in Context

Problema e solução em inglês, como no livro original.

A car leaves an intersection. The distance it travels in miles is given by the function $f (t),$ where $t$ represents hours. Explain the following notations:

ⓐ $f (0) = 0$
ⓑ $f^{'} (1) = 60$
ⓒ $f (1) = 70$
ⓓ $f (2.5) = 150$

Resolva no papel primeiro. Depois abra a solução um passo de cada vez e pare assim que conseguir terminar sozinho.

1
Solução
First we need to evaluate the function $f (t)$ and the derivative of the function $f^{'} (t),$ and distinguish between the two. When we evaluate the function $f (t),$ we are finding the distance the car has traveled in $t$ hours. When we evaluate the derivative $f^{'} (t),$ we are finding the speed of the car after $t$ hours.
1. ⓐ $f (0) = 0$ means that in zero hours, the car has traveled zero miles.
2. ⓑ $f^{'} (1) = 60$ means that one hour into the trip, the car is traveling 60 miles per hour.
3. ⓒ $f (1) = 70$ means that one hour into the trip, the car has traveled 70 miles. At some point during the first hour, then, the car must have been traveling faster than it was at the 1-hour mark.
4. ⓓ $f (2.5) = 150$ means that two hours and thirty minutes into the trip, the car has traveled 150 miles.

Sua vez

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A runner runs along a straight east-west road. The function $f (t)$ gives how many feet eastward of her starting point she is after $t$ seconds. Interpret each of the following as it relates to the runner.

ⓐ $f (0) = 0$
ⓑ $f (10) = 150$
ⓓ $f^{'} (20) = - 10$
ⓔ $f (40) = −100$

Como foi?

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O Try It do livro logo depois deste exemplo: mesma ideia, outros números. Só a resposta é dada.

ⓐ $f (0) = 0$
ⓑ $f (10) = 150$
ⓓ $f^{'} (20) = - 10$
ⓔ $f (40) = −100$

Solução

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Solução

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