f ( x ) = x 2 + 9 f or e a c h x ∈ R x 2 ≥ 0 ⇒ x 2 + 9 ≥ 9 ⇒ f ( x ) ≥ 9 y min = 9 y ma x → n o t e x i s t
0 \Rightarrow \hbox{no maximum}"> a > 0 ⇒ no maximum
y min = 4 a − b 2 + 4 a c y min = 4 ⋅ 1 − 0 2 + 4 ⋅ 1 ⋅ 9 y min = 9
The minimum value of the function f ( x ) = x 2 + 9 is 9 , occurring at x = 0 . The function does not have a maximum value as it approaches infinity. Therefore, the maximum value does not exist.
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