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16 Mar 2018, 00:56
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[GMAT math practice question]
Suppose \(y=2^{x^2}+2^{x+3}\). Which of these \(x\)-values gives the smallest value of \(y\)?
A. -3
B. -2
C. -1
D. 1
E. 2
Suppose \(y=2^{x^2}+2^{x+3}\). Which of these \(x\)-values gives the smallest value of \(y\)?
A. -3
B. -2
C. -1
D. 1
E. 2
16 Mar 2018, 01:20
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MathRevolution
A. -3 y = 2^9 + 2^0 = 513
B. -2 y = 2^4 + 2^1 = 17
C. -1 y = 2^1 + 2^2 = 5
D. 1 y = 2^1 + 2^4 = 18
E. 2 y = 2^4 + 2^5 = 48
Answer: option C
18 Mar 2018, 23:21
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Since the exponent function \(y=2^x\) is an increasing function, the smallest value of \(x^2+2x+3\) gives the smallest value of \(y=2^{x^2}+2^{x+3}\).
Since \(x^2+2x+3 = (x+1)^2 + 2\), the exponent \((x+1)^2 + 2\) has a minimum value when \(x = -1\).
Therefore, the answer is C.
Answer : C
Since the exponent function \(y=2^x\) is an increasing function, the smallest value of \(x^2+2x+3\) gives the smallest value of \(y=2^{x^2}+2^{x+3}\).
Since \(x^2+2x+3 = (x+1)^2 + 2\), the exponent \((x+1)^2 + 2\) has a minimum value when \(x = -1\).
Therefore, the answer is C.
Answer : C
