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what is the greatest possible value of the function f(x)?

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what is the greatest possible value of the function f(x)? [#permalink] New post 07 Apr 2014, 02:47
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what is the greatest possible value of the function f(x)?

(1) f(x)=k-x^2

(2) the straightline distance between the two roots of f(x) is 6.


THE OA IS NOT PROVIDED

Last edited by venkateshreddy on 07 Apr 2014, 06:09, edited 1 time in total.
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Re: what is the greatest possible value of the function f(x)? [#permalink] New post 07 Apr 2014, 03:34
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(1) If x^2 = 0, f(x)=k. This is the largest value as x^2 can't be negative. SUFFICIENT.

(2) Roots of an equation: f(x) = 0. We know nothing about this maximum. NOT SUFFICIENT.

(A)
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Re: what is the greatest possible value of the function f(x)? [#permalink] New post 08 Apr 2014, 08:25
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slemtem wrote:
(1) If x^2 = 0, f(x)=k. This is the largest value as x^2 can't be negative. SUFFICIENT.

(2) Roots of an equation: f(x) = 0. We know nothing about this maximum. NOT SUFFICIENT.

(A)


In GMAT, until you get a singular numerical value, that statement is not sufficient.

From F.S 1, we know that \(f(x) = k-x^2\) . Now, the largest value of f(x) would be at x=0, however, that value would be 'k' and this is not a numerical value. Insufficient.

From F.S 2, we know that the difference between the roots of f(x) is 6. The is clearly Insufficient.

Taking both together, we know that for y=0, we have \(x^2= k\) and the roots are = \(\pm\sqrt{k}.\)

Also, \(|\sqrt{k}-(-\sqrt{k})| = 6\) -->\(2\sqrt{k}\)= 6. We know the value of 'k'. Sufficient.

C.
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Re: what is the greatest possible value of the function f(x)? [#permalink] New post 08 Apr 2014, 15:38
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Question asks - do we have enough information to calculate maximum value of some function.

1) we don't know what k is therefore we cannot know the value of f(x) (INS)
2) we do not know what f(x) is so distance between roots is meaningless. (INS)

1+2) knowing that \(f(x)= -x^2 + k\), we know that equation has 2 roots.
we can rewrite the function as: \((\sqrt{k}+x)(\sqrt{k}-x)=0\)
\(x=\sqrt{k}\) or \(x=-\sqrt{k}\)
in order to achieve distance of 6, each root's absolute value needs to be 3. 6/2=3. So our roots are 3 and -3 on a parabola and k=9
Knowing k we can calculate \(f(x)=-x^2+9\)

Sufficient: C
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Re: what is the greatest possible value of the function f(x)? [#permalink] New post 06 Jun 2014, 04:47
venkateshreddy wrote:
what is the greatest possible value of the function f(x)?

(1) f(x)=k-x^2

(2) the straightline distance between the two roots of f(x) is 6.


THE OA IS NOT PROVIDED



We have to find the max possible value for the function. which is possible when x= 0 or x^2= 0

but we have found the value of x = 3 and -3 and corresponding value of k = 9

shouldn't we have found the value of K when x= 0 to show the max value of the function?

This is a different kind of sum which I am not able to fully comprehend? also here, is f(x) the equation of a parabola?

Can some one more clarify this for me.
Thank you
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what is the greatest possible value of the function f(x)? [#permalink] New post 21 Oct 2014, 00:46
qlx wrote:
venkateshreddy wrote:
what is the greatest possible value of the function f(x)?

(1) f(x)=k-x^2

(2) the straightline distance between the two roots of f(x) is 6.


THE OA IS NOT PROVIDED



We have to find the max possible value for the function. which is possible when x= 0 or x^2= 0

but we have found the value of x = 3 and -3 and corresponding value of k = 9

shouldn't we have found the value of K when x= 0 to show the max value of the function?

This is a different kind of sum which I am not able to fully comprehend? also here, is f(x) the equation of a parabola?

Can some one more clarify this for me.
Thank you





Yes QLX ... Your approach is correct. In your approach also you are getting option C as correct which is indeed the right answer.

You are also correct when you say that it the equation of the parabola.

Parabola eq: f(x)=y=a(x^2) + bx + c

Comparing it with f(x)=k-x^2 :

We get 'b' is zero. And since 'a' is negative , we get a parabola that opens downward.

In a parabola equation, to get x-intercepts(i.e roots) , put y=0. And we get +/- sq. root of k ---> So the parabola cuts the x axis at two places.
The distance between these roots is mentioned as 6. So sq. root of k= 3.. Then k=9.

Now the point on y axis where x =0 will be the maximum value for the function. i.e. y=k .. Hence y=9 is maximum value.


This is the method to solve through parabola.

You just solved it in a different way, but yours is also correct
what is the greatest possible value of the function f(x)?   [#permalink] 21 Oct 2014, 00:46
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