MathDB
Problems
Contests
National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
2006 Swedish Mathematical Competition
3
3
Part of
2006 Swedish Mathematical Competition
Problems
(1)
Sum of Slopes at Roots
Source: 2006 Swedish Mathematical Competition #3
1/5/2018
A cubic polynomial
f
f
f
with a positive leading coefficient has three different positive zeros. Show that
f
′
(
a
)
+
f
′
(
b
)
+
f
′
(
c
)
>
0
f'(a)+ f'(b)+ f'(c) > 0
f
′
(
a
)
+
f
′
(
b
)
+
f
′
(
c
)
>
0
.
analytic geometry
graphing lines
slope
calculus
derivative
algebra
Sweden