Problem: The smallest value of x2+8xx^{2}+8 xx2+8x for real values of xxx is
Answer Choices:
A. −16.25-16.25−16.25
B. −16-16−16
C. −15-15−15
D. −8-8−8
E. None of these Solution:
x2+8x=(x+4)2−16x^{2}+8 x=(x+4)^{2}-16x2+8x=(x+4)2−16 which is least (−16)(-16)(−16) when (x+4)2=0(x+4)^{2}=0(x+4)2=0 or when x=−4x=-4x=−4.