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{f{{({x})}}}={|{a}{x}-{b}|}+{c}{|{x}|}{x}{(-,)}, where {a}>{0}

Question

$f (x) = ∣ a x - b ∣ + c ∣ x ∣ \forall x \in (- \infty, \infty),$ where $a > 0, b > 0, c > 0 .$ Find the condition if $f (x)$ attains the minimum value only at one point.

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f (x) = ∣ a x - b ∣ + c ∣ x ∣ \forall x \in (- \infty, \infty),

where

a > 0, b > 0, c > 0 .

Find the condition if

f (x)

attains the minimum value only at one point.

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Question Text

f (x) = ∣ a x - b ∣ + c ∣ x ∣ \forall x \in (- \infty, \infty),

where

a > 0, b > 0, c > 0 .

Find the condition if

f (x)

attains the minimum value only at one point.

Filo tutor solution