# BC Calculus: Graphing f From Information About f' and f''

• Class: 5H: BC Calculus
• Author: Peter Atlas
• Text: Calculus Finney, Demana, Waits, Kennedy

1. Given the following table of values, graph a continuous function $$f$$.
$$x < -4$$ $$x = -4$$ $$-4 < x < 2$$ $$x = 2$$ $$x \gt 2$$
$$f'$$
+
1
+
DNE
-
$$f''$$
-
0
+
DNE
+
2. Solution
3. Given the following table of values, graph a continuous function $$f$$.
$$x < -1$$ $$x = -1$$ $$-1 < x < 1$$ $$x = 1$$ $$x \gt 1$$
$$f'$$
+
DNE
+
0
-
$$f''$$
+
DNE
-
-2
-
4. Solution
5. Given the following table of values, indicate where $$f$$ has relative extrema.
$$x = 2$$ $$2 < x < 5$$ $$x = 5$$ $$5 < x < 8$$ $$x = 8$$
$$f'$$
+
+
0
-
-
6. Solution $$f$$ has relative mins at $$x = 2$$ and $$x = 8$$ and a relative max at $$x = 5$$.