Function

[Michael_Light]

1. The problem statement, all variables and given/known data

Given http://www.mathhelpforum.com/math-help/attachments/f33/20928d1298610998-function-msp281219ebge8he857gc6900005ba9285dff0f5h79.gif , find the values of ''a'' for which the value of the function f(x) <= 25/2.

The answer is a<= 1/2.

2. Relevant equations



3. The attempt at a solution

I have no ideas how to eliminate the x, i can't solve it cause there are 2 unknown in one inequality...

[tiny-tim]

Hi Michael! :smile:

(have an leq: ≤ and try using the X2 icon just above the Reply box :wink:)
… find the values of ''a'' for which the value of the function f(x) <= 25/2.
…
I have no ideas how to eliminate the x, i can't solve it cause there are 2 unknown in one inequality...

It means find a such that the maximum value of f(x) is 25/2.

Hint: complete the square :wink:

[Michael_Light]

Hi Michael! :smile:

(have an leq: ≤ and try using the X2 icon just above the Reply box :wink:)


It means find a such that the maximum value of f(x) is 25/2.

Hint: complete the square :wink:

How do you know that it is a maximum but not minimum? :confused: By letting the maximum of f(x) = 25/2, i got a=1/2, what should i do next?

[tiny-tim]

By letting the maximum of f(x) = 25/2, i got a=1/2, what should i do next?

That sounds like an answer. :confused:

How did you get it?

Doesn't the way you got it tell you whether it's a maximum or minimum?

[Michael_Light]

Hi Michael! :smile:

(have an leq: ≤ and try using the X2 icon just above the Reply box :wink:)


It means find a such that the maximum value of f(x) is 25/2.

Hint: complete the square :wink:

I mean... how do you know that it is a maximum value before you find ''a''? and does f(x) <= 25/2
indicates that the maximum/minimum value of f(x) is smaller or equal than 25/2? Thanks.:smile:

[tiny-tim]

I've no idea what you've done. :confused:
… i got a=1/2 …

how did you get a = 1/2 ?

[Michael_Light]

I've no idea what you've done. :confused:


how did you get a = 1/2 ?

Max/min value of f(x), i.e -b2/4a + c = 25/2 and solve it....

[tiny-tim]

Max/min value of f(x), i.e -b2/4a + c = 25/2 ....

Is this just a formula that you've learnt from somewhere, or do you know how to prove it?

[Michael_Light]

Is this just a formula that you've learnt from somewhere, or do you know how to prove it?

By solving 32536.. i managed to get a=1/2, but yet the answer is a<= 1/2... i don't know why a <= 1/2...

[tiny-tim]

Do you know how to prove this formula??

Where did you get it from? :confused:

[Michael_Light]

Do you know how to prove this formula??

Where did you get it from? :confused:

From http://www.mathhelpforum.com/math-help/attachments/f33/20928d1298610998-function-msp281219ebge8he857gc6900005ba9285dff0f5h79.gif , we get f(x)=(a-1)x2+(4a+3)x+(4a-2)... where A represents (a-1), B represents (4a+3) and C represents (4a-2)... so -B2/4A + C = maximum/minimum value of f(x)...

[tiny-tim]

From … we get f(x)=(a-1)x2+(4a+3)x+(4a-2)... where A represents (a-1), B represents (4a+3) and C represents (4a-2)... so -B2/4A + C = maximum/minimum value of f(x)...

Yes, I know you can apply the formula (-B2/4A + C), but can you prove it?

Where did you get it from?

[Michael_Light]

Yes, I know you can apply the formula (-B2/4A + C), but can you prove it?

Where did you get it from?

From my reference book. :biggrin:

[tiny-tim]

ok then! :smile:

take the equation ax2 + bx + c = 0 and complete the square …

what do you get? :smile:

[Michael_Light]

ok then! :smile:

take the equation ax2 + bx + c = 0 and complete the square …

what do you get? :smile:

Someone clarified it for me... I managed to solve it now... Thanks for your time and patient.. :biggrin: