In this lab you will practice distinguishing between applications of the function and applications of the derivative.

Using SageMath to Calculate Derivatives and to Solve Equations

The first SageMath app below takes a function \(f(t)\) and a value \(t=a\) and computes both \(f(a)\) and the derivative of \(f(t)\) at \(t=a\), \(f'(a)\). The second SageMath app below is an equation solver. Use these apps to answer the questions below.

Note that the equal sign has different meanings in SageMath; either assigning the left-hand side of the equation to the right-hand side or the equality in an equation. For this reason, in the second app below, SageMath needs to use something besides ‘=’. The developers of SageMath have chosen the double equal sign ‘==’ to denote the equality in an equation.

1. In a medical experiment, the body weight in grams of a baby rat after \(t\) days was \(f(t)\) grams, where \(f(t)\) is specified in your lab report. Use the SageMath apps below to answer the following questions. Only use solutions that make sense in the context of the experiment and include brief explanations with your answers.