Math  /  Calculus

QuestionWhere on (,0)(-\infty, 0) does f(x)=25x2+3x+9xf(x)=\frac{25 x^{2}+3 x+9}{x} take its maximum value, and what is this maximum value?

Studdy Solution
Since f(x) f(x) approaches negative infinity as x0 x \to 0^- and as x x \to -\infty , the maximum value on (,0) (-\infty, 0) is at the critical point x=35 x = -\frac{3}{5} .
The maximum value of f(x) f(x) is 27 \boxed{-27} .

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