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uppose y=2^x^2+2^x+3. Which of these x-values gives the smal

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by Max@Math Revolution » Thu Mar 15, 2018 11:46 pm
[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
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by GMATinsight » Fri Mar 16, 2018 3:24 am
Max@Math Revolution wrote:[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
Checking options is the best way forward.

@Option C, $$y=2^{x^2}+2^{x+3}$$ . is minimum and is equal to 5

Answer: Option C
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by Max@Math Revolution » Sun Mar 18, 2018 10:09 pm
=>
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
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