WOLFRAM|DEMONSTRATIONS PROJECT

Instantaneous Rate of Change

​
x
0
-6
-4
-2
2
4
6
x
-40
-20
20
40
60
80
y
f(x)-x
3
+x
2
+12x-3
k = 12

This Demonstration shows the instantaneous rate of change for different
x
0
values of a cubic polynomial. Use the sliders to explore the special points. Also, find
x
values so that the polynomial has a given instantaneous rate of change, say
k=-12
.