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Spain Mathematical Olympiad
1966 Spain Mathematical Olympiad
8
8
Part of
1966 Spain Mathematical Olympiad
Problems
(1)
ax^3 + bx^2 + cx inflection point
Source: Spanish Mathematical Olympiad 1966 P8
12/4/2022
Determine the values of
a
,
b
,
c
a, b, c
a
,
b
,
c
, so that the graphical representation of the function
y
=
a
x
3
+
b
x
2
+
c
x
y = ax^3 + bx^2 + cx
y
=
a
x
3
+
b
x
2
+
c
x
has an inflection point at the point of abscissa
x
=
3
x = 3
x
=
3
, with tangent at the point of equation
x
ā
4
y
+
1
=
0.
x - 4y + 1 = 0.
x
ā
4
y
+
1
=
0.
Then draw the corresponding graph.
function
algebra
analysis