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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
If f(x)=x^2/b^2 + 2x + 4, then for each non-zero value of b the functi
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24 Aug 2021, 05:20
24 Aug 2021, 05:20
Expert Reply
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Question Stats:
90% (01:17) correct
9% (00:46) wrong based on 11 sessions
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If \(f(x)=\frac{x^2}{b^2} + 2x + 4\), then for each non-zero value of b the function of f(x) is the least when x equals
A. \(-1 -\sqrt{(1-4b)}\)
B. -2
C. 0
D. -b^2
E. b-4
A. \(-1 -\sqrt{(1-4b)}\)
B. -2
C. 0
D. -b^2
E. b-4
Re: If f(x)=x^2/b^2 + 2x + 4, then for each non-zero value of b the functi
[#permalink]
29 Aug 2021, 14:33
29 Aug 2021, 14:33
2
Expert Reply
\(f(x)=\frac{x^2}{b^2} + 2x + 4\) --> add b^2-b^2 --> \(f(x)=\frac{x^2}{b^2} + 2x + b^2 +4 -b^2\) --> \(f(x)=(\frac{x}{b})^2+ 2x + b^2 +4 -b^2\) --> \(f(x)=(\frac{x}{b}+b)^2+(4 -b^2)=(non-negative)+(constant)\).
The least value of f(x) when \((\frac{x}{b}+b)^2=0\), so when \(\frac{x}{b}+b=0\) or when \(x=-b^2\).
Answer: D.
The least value of f(x) when \((\frac{x}{b}+b)^2=0\), so when \(\frac{x}{b}+b=0\) or when \(x=-b^2\).
Answer: D.
gmatclubot
Re: If f(x)=x^2/b^2 + 2x + 4, then for each non-zero value of b the functi [#permalink]
29 Aug 2021, 14:33
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