sir similarily, for |3x+5| – |5x+3|, minimum value will be not defined as in – infinity but max will be 16/5,by putting the critical value for |5x+3| i.e. -3/5 in the eqn..is that right sir?
sir what if we have addition and subtraction in the same function?
Jaspreet, your answer is correct. We will look at a couple of more complicated examples in the next two posts, which will hopefully clarify what happens when more than two moduli are involved…
Sir, so basically if we are adding two modulus functions then we will get a minima and when we are subtracting two modulus functions we will get a maxima?
how to check the same if we are working with three modulus functions having alternate postive, negative signs?
Not exactly, Jim. When adding, we will get a minimum. When subtracting, it depends which has the higher slope (coefficient of x) so if it is |3x + 2| – |2x – 5| then the +ve modulus has a greater slope and hence there will be a minimum (just like a normal +ve modulus) but if it is |2x + 3| – |5x + 7| then the negative modulus has a higher slope and hence we will get a maximum.
For three or more moduli, the cumulative slopes will throw us a hint. For example for |2x + 3| + |6x + 2| – |4x + 5| – |5x – 3| the slopes are 2 +6 – 4 – 5 which gives -1 so it will have a maximum (similar to a normal modulus of the form -|x|)
And what is that “little thought” which will tell us at which end the minimum will lie ? I’m asking this so that I can have an idea of the graph without even plotting it. (might help other types of questions)
If that’s confusing then leave it 😛
Since the slope between the two values is negative, it will slope downwards towards the minimum value.
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