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

Watch
Announcements

Report

#2

(Original post by

What is the maximum value of 2sin^x - sinx + 1/3

**Carman3**)What is the maximum value of 2sin^x - sinx + 1/3

0

reply

(Original post by

Draw it?

**CheeseIsVeg**)Draw it?

0

reply

Report

#4

(Original post by

What is the maximum value of 2sin^x - sinx + 1/3

**Carman3**)What is the maximum value of 2sin^x - sinx + 1/3

0

reply

Report

#5

(Original post by

I dont know how to draw it all together

**Carman3**)I dont know how to draw it all together

Is this A-level?

0

reply

(Original post by

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).

**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).

0

reply

Report

#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.

0

reply

Report

#8

(Original post by

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?

**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?

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.

0

reply

(Original post by

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.

**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.

0

reply

Report

#10

(Original post by

Can you show me how to do it i cant get it

**Carman3**)Can you show me how to do it i cant get it

So first, complete the square. Then think about which value of between and (inclusive) is going to maximise the function.

0

reply

(Original post by

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.

**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.

0

reply

Report

#12

(Original post by

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

**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

0

reply

Report

#13

(Original post by

What is the maximum value of 2sin^x - sinx + 1/3

**Carman3**)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 constant

Solution

1

reply

Report

#15

(Original post by

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

**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

0

reply

**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

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

0

reply

Report

#17

(Original post by

Yep good approach for this particular problem but OP should remember that this method does not work in general for similar functions.

**IrrationalRoot**)Yep good approach for this particular problem but OP should remember that this method does not work in general for similar functions.

0

reply

Report

#18

**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.

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.

0

reply

Report

#19

(Original post by

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.

**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.

0

reply

Report

#20

(Original post by

Yeah that's true, but I was trying to show them explicitly how this works.

**IrrationalRoot**)Yeah that's true, but I was trying to show them explicitly how this works.

0

reply

X

### Quick Reply

Back

to top

to top