Question

|x - 1|+ |x – 2| + |x–3|+...+|x – 2019| + |x– 2020|.<br />Determine the greatest interval of real numbers [a, b] on which the given expression has a constant value k for all x € [a, b].<br />What is the value of k?​

Answer 1

Answer:

f(x)=ln{g(x)}

g(x)=e

f(x)

g

′

(x)=e

f(x)

.f

′

(x)

g

′

(x)=0⇒f

′

(x)=0 as

e

f(x)



=0

⇒2010(x−2009)(x−2010)

2

(x−2011)

3

(x−2012)

4

=0

so there is only one point of local maxima