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Find the maximum and minimum values, if any, of the following functions given by f (x) = – (x – 1) ^2 + 10

1. Find the maximum and minimum values, if any, of the following functions
given by

(iii) f (x) = - (x -1) ^2 + 10

Answers (1)
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Given function is,
f (x) = - (x -1) ^2 + 10
-(x-1)^2 \leq 0\\ -(x-1)^2+10\leq 10    for every x \ \epsilon \ R
Hence, maximum value occurs when 
(x-1)=0\\ x = 1
Hence, maximum value of function f (x) = - (x -1) ^2 + 10  occurs at  x = 1
and the maximum value is 
f(1) = -(1-1)^2+10=10 \\
            
and it is clear that there is no minimum value of  f (x) = 9x^2+12x+2

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