798

Part of 2012 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 798

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

C,\ l

the graphs of the cubic function

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

l: y=ax

.
(1) Find the range of

a

C

l

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

S(a)

by the area bounded by

C

l

a

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

a

S(a)

is minimized.
50 points

calculusintegrationfunctiongeometryderivativequadraticsanalytic geometry