+0  
 
0
31
1
avatar

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

Guest May 3, 2018

Best Answer 

 #1
avatar+92441 
+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.

Melody  May 3, 2018
Sort: 

1+0 Answers

 #1
avatar+92441 
+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

22 Online Users

New Privacy Policy (May 2018)
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  Privacy Policy