f, f', f'' Card Match (using the first and second derivative to graph f)

I use this activity after students have learned the power rule, and as they’re beginning to understand the relationship between f, f', and f''. Students find f' and f'' using the power rule, then use the graphs of f' (the derivative) and f'' (the second derivative) to graph f. They must use the idea that when f' is positive, f is increasing, and when f' is negative, f is decreasing, as well as connecting f'' to intervals of concavity on f. There are 48 total cards per set- 8 functions and their first and second derivative equations as well as graphs. Appropriate for any level of Calculus (including AP).

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