WOLFRAM|DEMONSTRATIONS PROJECT

Derivatives of Quintic Polynomials

​
coefficient of
5
x
-3
4
x
2
3
x
3
2
x
5
x
3
constant term
4
interval -10 ≤ x ≤ 10
x
2
reset
F(x) = -3
5
x
+2
4
x
+3
3
x
+5
2
x
+3x+4
The first derivative is:
′
F
(x) = -15
4
x
+8
3
x
+9
2
x
+10x+3
For x equal to 2,
′
F
(2) = -117
The second derivative is:
′′
F
(x) = -60
3
x
+24
2
x
+18x+10
For x equal to 2,
′′
F
(2) = -338
The third derivative is:
(3)
F
(x) = -180
2
x
+48x+18
For x equal to 2,
(3)
F
(2) = -606
The fourth derivative is:
(4)
F
(x) = 48-360x
For x equal to 2,
(4)
F
(2) = -672
This Demonstration calculates the first four derivatives of
F(x)=
c
5
5
x
+
c
4
4
x
+
c
3
3
x
+
c
2
2
x
+
c
1
x+
c
0
and evaluates them at
x
for
-10≤x≤10
.