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(38​x−x2)=3(916​−916​+38​x−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​.