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Maximum value of 2sin^x - sinx + 1/3?
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#2
(Original post by Carman3)
What is the maximum value of 2sin^x - sinx + 1/3
What is the maximum value of 2sin^x - sinx + 1/3
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(Original post by CheeseIsVeg)
Draw it?
Draw it?
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#4
(Original post by Carman3)
What is the maximum value of 2sin^x - sinx + 1/3
What is the maximum value of 2sin^x - sinx + 1/3
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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#5
(Original post by Carman3)
I dont know how to draw it all together
I dont know how to draw it all together
Is this A-level?
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(Original post by IrrationalRoot)
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).
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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#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.
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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#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?
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?
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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(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.
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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#10
(Original post by Carman3)
Can you show me how to do it i cant get it
Can you show me how to do it i cant get it
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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(Original post by IrrationalRoot)
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.
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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#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
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
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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#13
(Original post by Carman3)
What is the maximum value of 2sin^x - sinx + 1/3
What is the maximum value of 2sin^x - sinx + 1/3
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 constantSolution
Spoiler: 
and hence 
, meaning that the maximum value of 
is 2.
As we are subtracting
we want its smallest value. 
and hence we are using the value of to be -1.
We cannot change and hence our maximum value is 
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and hence , meaning that the maximum value of is 2.As we are subtracting
we want its smallest value. and hence we are using the value of to be -1.We cannot change
and hence our maximum value is
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#15
(Original post by some-student)
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
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 constantSolution
Spoiler: and hence , meaning that the maximum value of is 2.
As we are subtracting we want its smallest value. and hence we are using the value of to be -1.
We cannot change and hence our maximum value is
Show
and hence , meaning that the maximum value of is 2.As we are subtracting
we want its smallest value. and hence we are using the value of to be -1.We cannot change
and hence our maximum value is
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(Original post by some-student)
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
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 constantSolution
Spoiler: and hence , meaning that the maximum value of is 2.
As we are subtracting we want its smallest value. and hence we are using the value of to be -1.
We cannot change and hence our maximum value is
Show
and hence , meaning that the maximum value of is 2.As we are subtracting
we want its smallest value. and hence we are using the value of to be -1.We cannot change
and hence our maximum value is 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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#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.
Yep good approach for this particular problem but OP should remember that this method does not work in general for similar functions.
, it lines up with 
, and this isn't always the case.
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#18
(Original post by IrrationalRoot)
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.
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.
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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#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.
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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#20
(Original post by IrrationalRoot)
Yeah that's true, but I was trying to show them explicitly how this works.
Yeah that's true, but I was trying to show them explicitly how this works.
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