(2 pts) Below is an \"oracle\" function. An oracle function is a function presen

Question

(2 pts) Below is an "oracle" function. An oracle function is a function presented interactively. When you type in a t value, and press the button the value f(t) appears in the right hand window. There are three lines, so you can calculate three different values of the function at one time. Average velocity at 0.47- You can use a calculator 0.47 0.47 0.47 Think of velocity as a change in position over time. Thus, you can find an average velocity over a small window of time. Hint: Think slopel Remember this technique for finding velocities. Later we will use the same method to find the derivative of functions such as f(t).

Explanation / Answer

Ans. To find the average velocity at time t = 0.47 s , first we find the height i.e f(t) at two values of time around t = 0.47 s. We also need f(t) at t = 0.47 s. You can find the values of f(t) using oracle. Put t = 0.46sec, 0.47 s and 0.48 s into the table and get f(t) at these values.

Now average velocity at t = 0.47 s can be => f(0.47-) = [f(0.46) - f(0.47)]/(0.46 - 0.47)

or ===> f(0.47+) = [f(0.48) - f(0.47)]/(0.48 - 0.47)

You find both of these and take average of these two i.e Vavg = [f(0.47-) + f(0.47+)] / 2

You can get a better approximation if we take the two values of t more closer to 0.47s and if you can take close enough value of t(i.e t = 0.469 s or t= 0.471 s or more closer) around t = 0.47 s then you need not find both f(0.47+) and f(0.47-) and average them, just find one and that should be average velocity.

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