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"> a > 0 so the function has a minimum, but no maximum.
The function f ( x ) = x 2 + 9 has a minimum value of 9 at x = 0 and does not have a maximum value, as it continues to increase indefinitely. The parabola opens upwards, confirming that a minimum is present. Thus, the only extremum for this function is a minimum at ( 0 , 9 ) .
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