Problem: For any real value of x the maximum value of 8x−3x2 is:
Answer Choices:
A. 0
B. 38
C. 4
D. 5
E. 316
Solution:
Transform the expression 8x−3x2 into
3(38x−x2)=3(916−916+38x−x2)
=3[916−(x−34)2]=316−3(x−34)2.
The maximum value of this last expression occurs when the term −3(x−34)2 is zero. Therefore, the maximum value of 8x−3x2 is 316
or
Let y=−3x2+8x. When graphed this equation represents a parabola with a highest point at (34,316). Therefore, the maximum value of - 3x2+8x is 316.