# Maximum value of 2sin^x - sinx + 1/3?

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#1
What is the maximum value of 2sin^x - sinx + 1/3
0
4 years ago
#2
(Original post by Carman3)
What is the maximum value of 2sin^x - sinx + 1/3
Draw it?
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#3
(Original post by CheeseIsVeg)
Draw it?
I dont know how to draw it all together
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4 years ago
#4
(Original post by Carman3)
What is the maximum value of 2sin^x - sinx + 1/3
Notice that the given expression is just a function of so the question is equivalent to 'What is the maximum value of ?' where is restricted to a certain interval (which you know).
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4 years ago
#5
(Original post by Carman3)
I dont know how to draw it all together
Ok, first, in the question did they say to use any particular methods etc?
Is this A-level?
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#6
You cant factorise the y equation so how do you do it... Plus its a positive quadratic so it wouldnt have a maximum would it?
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4 years ago
#7
First consider the variable factor sin(x) usually you would consider sin(x) = 1, sin(x) =0 or sin(x) =-1 to see which one gives the maximum value.
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4 years ago
#8
(Original post by Carman3)
You cant factorise the y equation so how do you do it... Plus its a positive quadratic so it wouldnt have a maximum would it?
Factorising has nothing to do with locating maxima/minima. You would complete the square to find the maximum/minimum of a quadratic (this is basic C1 knowledge, but not sure what stage you're at in school).

And yes it's a positive quadratic but I did mention that i.e. is restricted to a certain interval that you know, so it has a maximum.
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#9
(Original post by IrrationalRoot)
Factorising has nothing to do with locating maxima/minima. You would complete the square to find the maximum/minimum of a quadratic (this is basic C1 knowledge, but not sure what stage you're at in school).

And yes it's a positive quadratic but I did mention that i.e. is restricted to a certain interval that you know, so it has a maximum.
Can you show me how to do it i cant get it
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4 years ago
#10
(Original post by Carman3)
Can you show me how to do it i cant get it
You're trying to maximise the function with the restriction that .

So first, complete the square. Then think about which value of between and (inclusive) is going to maximise the function.
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#11
ok i get it thanks. how do you know if they are talking about the max/min value which would be the vertex or the maximum/min overall value like the above
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4 years ago
#12
(Original post by Carman3)
ok i get it thanks. how do you know if they are talking about the max/min value which would be the vertex or the maximum/min overall value like the above
It's not about which one they're talking about, it's about what the function is. is not the same function as (which is a parabola with a vertex and such). It's just that the maximum of is going to be the same as that of the function restricted to , since sine can only take those values.
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4 years ago
#13
(Original post by Carman3)
What is the maximum value of 2sin^x - sinx + 1/3
To get the maximum value:
we want the maximum value of we want the minimum value of as we are subtracting it from our maximum of we cannot change as it is a constant

Solution
1
4 years ago
#14
i would use differentiation 0
4 years ago
#15
Yep good approach for this particular problem but OP should remember that this method does not work in general for similar functions.
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#16
Thanks...
Dont answer the question from the paper as i havent tried it yet but would you also do the same for this: and similar questions as well

https://s3-eu-west-1.amazonaws.com/w...56dfc5cd_1.pdf

Question 1E
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4 years ago
#17
(Original post by IrrationalRoot)
Yep good approach for this particular problem but OP should remember that this method does not work in general for similar functions.
Yeah - I should comment that this problem only happens as when , it lines up with , and this isn't always the case.
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4 years ago
#18
I don't see a need to complete the square here, although it is a technique that you need to know and is useful for sketching the function.

As it's a parabola with a positive coefficient, you know that the maximum value over any range is going to be at the end of the range. For a symmetric range, the negative coefficient tells you which end, or simply trying the two values.
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4 years ago
#19
(Original post by RogerOxon)
I don't see a need to complete the square here, although it is a technique that you need to know and is useful for sketching the function.

As it's a parabola with a positive coefficient, you know that the maximum value over any range is going to be at the end of the range. For a symmetric range, the negative coefficient tells you which end, or simply trying the two values.
Yeah that's true, but I was trying to show them explicitly how this works.
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4 years ago
#20
(Original post by IrrationalRoot)
Yeah that's true, but I was trying to show them explicitly how this works.
Fair enough.
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