A quadratic function f(x) attains a maximum value of 3 at x=1. The value of the function at x=0 is 1.what is the value of f(x) at x =10 ?
a)-105
b)-119
c)-159
d)-110
e)-180
Functions
This topic has expert replies
-
- Senior | Next Rank: 100 Posts
- Posts: 46
- Joined: Sat Feb 27, 2010 2:58 am
- Location: GMAT
- sanju09
- GMAT Instructor
- Posts: 3650
- Joined: Wed Jan 21, 2009 4:27 am
- Location: India
- Thanked: 267 times
- Followed by:80 members
- GMAT Score:760
Let f (x) = a x^2 + b x + c is the quadratic function, such thatGMATSUCKER wrote:A quadratic function f(x) attains a maximum value of 3 at x=1. The value of the function at x=0 is 1.what is the value of f(x) at x =10 ?
a)-105
b)-119
c)-159
d)-110
e)-180
At x = 1, a + b + c = 3, and at x = 0, c = 1
Then, at x = 10, f (x) = a (10) ^2 + b (10) + c = 100 a + 10 b + c = 90 a + 21 (?);
but f (x) cannot exceed 3, hence a is a negative integer.
Under these restrictions, no choice other than [spoiler]C[/spoiler] can take 90 a + 21, which happens at a = -2.
[spoiler]C[/spoiler]
I preferred to EXPLOIT the choices in hand, instead of going through the ways which are either long or beyond the GMAT specifications.
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
-
- Senior | Next Rank: 100 Posts
- Posts: 46
- Joined: Sat Feb 27, 2010 2:58 am
- Location: GMAT
Any other approach to solve this problem ?
GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT
What's life without GMAT !!!!!!!!
What's life without GMAT !!!!!!!!
- harshavardhanc
- Legendary Member
- Posts: 526
- Joined: Sat Feb 21, 2009 11:47 pm
- Location: India
- Thanked: 68 times
- GMAT Score:680
nice approach!sanju09 wrote: Under these restrictions, no choice other than [spoiler]C[/spoiler] can take 90 a + 21, which happens at a = -2.
[spoiler]C[/spoiler]
I preferred to EXPLOIT the choices in hand, instead of going through the ways which are either long or beyond the GMAT specifications.
as said by sanju, the other methods to solve this problem will probably employ techniques that are beyond GMAT.GMATSUCKER wrote:Any other approach to solve this problem ?
For e.g.
generic quad eq f(x) = ax^2 + bx + c (observe that there are 3 variables)
now based on the question, you can easily get value of C =1 and another eq. which gives a+b=2.
what about the third eq ?
you will have to differentiate the quadratic eq. with respect to x ( a concept beyond the scope), which will give you :
maximum value of this quad eq. is at x= (-b/2a). which on further solving will give a=-2 and b=4.
Hence the quad function is y= -2x^2 + 4x +1
at x=10, the value will be -159.
But, as a point to remember you can keep this in mind :
would like to see any simpler methods.maximum/minimum value of a 2nd degree equation (quad function) in x represented by ax^2 + bx + c is at x= (-b)/2a
Regards,
Harsha
Harsha