+0  
 
0
167
1
avatar

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

 May 3, 2018

Best Answer 

 #1
avatar+94975 
+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+94975 
+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

6 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.