Another Rational Problem

[Jason76]

Post Edited

\(\displaystyle f(x) = \dfrac{6x^{2} + 8x + 6}{\sqrt{x}}\)

\(\displaystyle f(x) = \dfrac{6x^{2} + 8x + 6}{x^{1/2}}\)

\(\displaystyle f'(x) = \dfrac{6x^{2}}{x^{1/2}} + \dfrac{8x}{x^{1/2}} + \dfrac{6}{x^{1/2}} \)

\(\displaystyle f'(x) = 6x^{3/2} + x^{1/2} + 6x^{-1/2}\) Online homework says incorrect

 

[Deleted member 4993]

f(x) = \(\displaystyle \dfrac{6x^{2} + 8x + 6}{\sqrt{x}}\)

f'(x) = \(\displaystyle \dfrac{6x^{2} + 8x + 6}{x^{1/2}}\)..........................How did you get that from above??!!

\(\displaystyle f'(x) = \dfrac{6x^{2}}{x^{1/2}} + \dfrac{8x}{x^{1/2}} + \dfrac{6}{x^{1/2}} \)

\(\displaystyle f'(x) = 6x^{3/2} + x^{1/2} + 6x^{-1/2}\) Online homework says incorrect

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[Jason76]

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\(\displaystyle x^{1/2} = \sqrt{x}\)

 

[Deleted member 4993]

\(\displaystyle f(x) = \dfrac{6x^{2} + 8x + 6}{\sqrt{x}}\)

\(\displaystyle \frac{df(x)}{dx} = \) \(\displaystyle f'(x) = \dfrac{6x^{2} + 8x + 6}{x^{1/2}}\) .... Are you claiming that f(x) = \(\displaystyle \frac{df(x)}{dx} \)???

\(\displaystyle f'(x) = \dfrac{6x^{2}}{x^{1/2}} + \dfrac{8x}{x^{1/2}} + \dfrac{6}{x^{1/2}} \)

\(\displaystyle f'(x) = 6x^{3/2} + x^{1/2} + 6x^{-1/2}\) Online homework says incorrect

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[Jason76]

\(\displaystyle f(x) = \dfrac{6x^{2} + 8x + 6}{\sqrt{x}}\)

\(\displaystyle f(x) = \dfrac{6x^{2} + 8x + 6}{x^{1/2}}\)

\(\displaystyle f(x) = \dfrac{6x^{2}}{x^{1/2}} + \dfrac{8x}{x^{1/2}} + \dfrac{6}{x^{1/2}} \)

\(\displaystyle f(x) = 6x^{3/2} + x^{1/2} + 6x^{-1/2}\)

Next step, do derivative

 

[srmichael]

\(\displaystyle f(x) = \dfrac{6x^{2} + 8x + 6}{\sqrt{x}}\)

\(\displaystyle f(x) = \dfrac{6x^{2} + 8x + 6}{x^{1/2}}\)

\(\displaystyle f(x) = \dfrac{6x^{2}}{x^{1/2}} + \dfrac{8x}{x^{1/2}} + \dfrac{6}{x^{1/2}} \)

\(\displaystyle f(x) = 6x^{3/2} + x^{1/2} + 6x^{-1/2}\) Online homework says incorrect

It's incorrect because you have not taken the derivative of it. Take the derivative THEN check your answer with the book's answer.

 

[Jason76]

\(\displaystyle f(x) = \dfrac{6x^{2} + 8x + 6}{\sqrt{x}}\)

\(\displaystyle f(x) = \dfrac{6x^{2} + 8x + 6}{x^{1/2}}\)

\(\displaystyle f(x) = \dfrac{6x^{2}}{x^{1/2}} + \dfrac{8x}{x^{1/2}} + \dfrac{6}{x^{1/2}} \)

\(\displaystyle f(x) = 6x^{3/2} + x^{1/2} + 6x^{-1/2}\)

\(\displaystyle f'(x) = (\dfrac{3}{2})6x^{1/2} + (\dfrac{1}{2})x^{-1/2} + (-\dfrac{1}{2})6x^{-3/2}\)

\(\displaystyle f'(x) = 9x^{1/2} + \dfrac{1}{2}x^{-1/2} - 3x^{-3/2} \) - Answer, I think