MathDB

Today's calculation of Integral 798

Source: 2012 Tokyo Institute of Technology entrance exam, problem 3

February 29, 2012

calculusintegrationfunctiongeometryderivativequadraticsanalytic geometry

Problem Statement

Denote by

C,\ l

the graphs of the cubic function

C: y=x^3-3x^2+2x

, the line

l: y=ax

.
(1) Find the range of

a

such that

C

and

l

have intersection point other than the origin.
(2) Denote

S(a)

by the area bounded by

C

and

l

. If

a

move in the range found in (1), then find the value of

a

for which

S(a)

is minimized.
50 points