An algebra problem by Rajdeep Dhingra

Algebra Level 2

T h e G r e a t e s t V a l u e A s s u m e d b y t h e F u n c t i o n f ( x ) = 5 − ∣ x − 3 ∣ i s : The\quad Greatest\quad Value\quad Assumed\quad by\quad the\quad Function\\ f(x)\quad =\quad 5\quad -\quad |x\quad -\quad 3|\quad is\quad :


The answer is 5.

Rajdeep Dhingra by Rajdeep Dhingra , 20, India

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2 solutions

Rajdeep Dhingra
Oct 17, 2014

T o f i n d M a x i m u m V a l u e W e w i l l d i f f e r e n t i a t e t h e f u n c t i o n a n d e q u a l i t t o 0 d d x ( 5 − ∣ x − 3 ∣ ) = 3 − x ∣ x − 3 ∣ = 0 3 − x = 0 x = 3 F i n d f ( 3 ) = 5 ( m a x ) To\quad find\quad Maximum\quad Value\quad We\\ will\quad differentiate\quad the\quad function\quad \\ and\quad equal\quad it\quad to\quad 0\\ \frac { d }{ dx } (5-\quad |x\quad -\quad 3|)\quad =\quad \frac { 3\quad -\quad x }{ |x\quad -\quad 3| } \quad =\quad 0\\ 3\quad -\quad x\quad =\quad 0\\ x\quad =\quad 3\\ Find\quad f(3)\\ =\quad 5\quad (max)

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Archit Boobna
Oct 17, 2014

We know that |x-3| can't be negative. So to find max value of 5- |x-3|, we have to get |x-3| to 0. Which gives us 5.

(Better and Simpler than Rajdeep's solution... )

2 Helpful 0 Interesting 0 Brilliant 1 Confused

Maximum occurs at x = 3 ∈ R x=3\in \mathbb{R} and is the equality case for the following inequality:

5 − ∣ x − 3 ∣ ≤ 5 5-|x-3|\leq 5

Prasun Biswas - 6 years, 3 months ago

I did it the same way

Abdur Rehman Zahid - 6 years, 7 months ago

rajdeep bhaiyua aap kis school mai padhte hai aap abhi bhi dps school mai padhte hai

Real Champ - 3 years, 11 months ago

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