MathDB

Today's calculation of Integral 290

Source: 2008 Keio University entrance exam/Pharmacy

February 6, 2008

calculusintegrationanalytic geometrygraphing linesslopegeometryderivative

Problem Statement

Let the curve C: y \equal{} |x^2 \plus{} 2x \minus{} 3| and the line

l

passing through the point ( \minus{} 3,\ 0) with a slope

m

in x\minus{}y plane. Suppose that

C

intersects to

l

at distinct two points other than the point ( \minus{} 3,\ 0), find the value of

m

for which the area of the figure bounded by

C

and

l

is minimized.