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Question 1966: State whether the following function has a maximum value or minimum value and find it? f(x)=2+10x - x^2 ( to the power of 2:forget it)
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! First of all you should know the basic common notation about the power.
Use complete square
f(x) = 2 + 10x - x^2 = -(x^2 - 10x + (10/2)^2) + 25 + 2
= 27 - (x - 5)^2
Since - (x - 5)^2 <= 0 for all real x, 27 - (x - 5)^2 <= 27 for all x.
Hence,when x = 5, f has maximum value 27.
Also, we see that f(x) approaches -oo as x-->+oo.
So,f has no minimum value.
Kenny
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