For $f(x) = x^{3.2}\times e^{-0.35x}$, at what $x$ value does the maximum occur

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For $f(x) = x^{3.2}\times \mathrm{e}^{-0.35x}$, at what $x$ value does the maximum occur

for minimum or maximum $f'(x)=0$

this implies $3.2 x^{2.2} \mathrm{e}^{-0.35x}-x^{3.2}\mathrm{e}^{-0.35x}\times 0.35=0$

I can't for further can any one help me

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2 Answers

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$$(x^ae^{-bx})'=ax^{a-1}e^{-bx}-bx^ae^{-bx}=(a-bx)x^{a-1}e^{-bx},$$ and the roots are obvious.

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we have by the product and power rule $$f'(x)=-\frac{1}{20} e^{-7 x/20} x^{11/5} (7 x-64)$$

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