Definition of Derivative Worksheet



Definition of Derivative Worksheet

Use the definition of a derivative [pic] to find the derivative of each function at the point indicated.

1. y = 2x2 – 5x – 4 at x = 5 2. y = [pic] at x = 3

Use our same limit of slopes definition to find the generalized derivative for the function. Remember that means your answer will be in terms of ‘t’.

3. h(t) = -16t² + 60t + 80

4. If the function in number 3 measures height (feet) in terms of time (sec), use your answer to find

a) the instantaneous velocity when t = 0

b) the instantaneous velocity when t = 1

c) the instantaneous velocity when t = 2

d) Now find the average velocity from t = [0,2]. (this is an easy calculation)

e) Compare the 3 instantaneous velocities with the average velocity you found.

f) Graph the original function on your calculator. Why do the veloctiies in a-d make sense in reference to the graph?

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