Ultimate Question 1

let
f(x)=âˆ«(0 to 1)|t-x|tdt
for all real x. What is the minimum value of f(x).

1 Answers

1357

Manish Shankar ·2013-02-04 21:51:53

f(x)=(1/3-x/2) x<0
f(x)=(x/2-1/3) x>1
f(x)=(x³/2 -x/2 +1/3 ) 0<x<1

Find the minima

For 0<x<1

write the integral as
âˆ«(0->x)(x-t)tdt+âˆ«(x->1)(t-x)tdt

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