Question
Question: The function f(x) = \|ax – b\| + c\|x\| ∀ x ∈ (-∞, ∞), where a \> 0, b \> 0, c \> 0, assumes it's mi...
The function f(x) = |ax – b| + c|x| ∀ x ∈ (-∞, ∞), where a > 0, b > 0, c > 0, assumes it's minimum value only at one point if
A
a ≠ b
B
a ≠ c
C
b ≠c
D
a = b = c
Answer
a = b = c
Explanation
Solution
f(x) =
These figures clearly indicate that for exactly one point of minima, a ≠ c.