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WOLFRAM|DEMONSTRATIONS PROJECT

A Fifth-Degree Polynomial and Its Derivatives

​
number of derivatives
0
1
2
3
4
from x = -4 to 4
This Demonstration displays the graph of the fifth-degree polynomial,
f(x)=0.01
5
x
-0.015
4
x
-0.21
3
x
+0.2
2
x
+0.5x-0.5
, and up to four of its derivatives. As you move the slider across, note how when the function (blue curve) goes down, the first derivative (orange) is below the
x
axis, and when the function has a maximum or minimum the first derivative crosses the
x
axis. Check how the second derivative (green) shows the concavity of the function. Why is the fourth derivative a straight line?
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