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  • The function <img alt="\mathrm{f(x)=|a x-b|+c|x| \forall x \in(-\infty, \infty)}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bf%28x%29%3D%7Ca%20x-b%7C&plus;c%7Cx%7C%20%5Cfo

The function \mathrm{f(x)=|a x-b|+c|x| \forall x \in(-\infty, \infty)}, where \mathrm{a>0, b>0, c>0}, assumes its minimum value only at one point if f(x)= \begin{cases}b-(a+c) x & , \quad x<0 \\ b+(c-a) x & , \quad 0 \leq x<\frac{b}{a} \\ (a+c) x+b & , \quad x \geq \frac{b}{a}\end{cases}

Option: 1

\mathrm{a \neq b}


Option: 2

\mathrm{a \neq c}


Option: 3

\mathrm{b \neq c}


Option: 4

\mathrm{a=b=c}


Answers (1)

best_answer



These figures clearly indicate that for exactly one point of minima, a \neq c.

Posted by

Suraj Bhandari

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