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If 54+9f(x)+x^2(f(x))^3=0 and f(1)=−3, find f′(1)

 May 3, 2018

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 #1
avatar+101741 
+2

If 54+9f(x)+x^2(f(x))^3=0 and f(1)=−3, find f′(1)

 

\(If \;\;\;54+9f(x)+x^2(f(x))^3=0 \quad and \quad f(1)=−3, \quad find\;\;f′(1)\\ let\;\;y=f(x)\\ 54+9y+x^2y^3=0\\ \text{differentiate wrt x}\\ 9y'+2xy^3+3x^2y^2y'=0\\ y'(9+3x^2y^2)+2xy^3=0\\ sub\;\;in\;\;x=1\;\;and\;\;f(1)=-3\\ f'(1)(9+3*1^2*(-3)^2)+2*1*(-3)^3=0\\ f'(1)(-18)+-54=0\\ f'(1)(-18)=54\\ f'(1)=-3 \)

 

I have done this with many distractions so you better check my working.

 May 3, 2018
 #1
avatar+101741 
+2
Best Answer

If 54+9f(x)+x^2(f(x))^3=0 and f(1)=−3, find f′(1)

 

\(If \;\;\;54+9f(x)+x^2(f(x))^3=0 \quad and \quad f(1)=−3, \quad find\;\;f′(1)\\ let\;\;y=f(x)\\ 54+9y+x^2y^3=0\\ \text{differentiate wrt x}\\ 9y'+2xy^3+3x^2y^2y'=0\\ y'(9+3x^2y^2)+2xy^3=0\\ sub\;\;in\;\;x=1\;\;and\;\;f(1)=-3\\ f'(1)(9+3*1^2*(-3)^2)+2*1*(-3)^3=0\\ f'(1)(-18)+-54=0\\ f'(1)(-18)=54\\ f'(1)=-3 \)

 

I have done this with many distractions so you better check my working.

Melody May 3, 2018

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