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March 1st, 2017, 02:35 PM  #1 
Newbie Joined: Feb 2017 From: Michigan Posts: 17 Thanks: 0  Can someone please help me answer this? thanks
Use the gradient to find the directional derivative of the function at P in the direction of Q. f(x, y) = 3x²  y² + 4, P(7, 5), Q(6, 8) Last edited by skipjack; March 1st, 2017 at 02:56 PM. 
March 1st, 2017, 02:58 PM  #2 
Member Joined: Oct 2016 From: Melbourne Posts: 77 Thanks: 35 
So can you get the gradient vector $\displaystyle \begin{align*} \nabla f \end{align*}$? Do you know how to use this to get the direction vector $\displaystyle \begin{align*} \frac{\mathrm{d}f}{\mathrm{d}\mathbf{u}} = \nabla f \cdot \hat{ \mathbf{u} } \end{align*}$?

March 1st, 2017, 03:01 PM  #3  
Newbie Joined: Feb 2017 From: Michigan Posts: 17 Thanks: 0  Quote:
Last edited by skipjack; March 3rd, 2017 at 04:36 PM.  
March 1st, 2017, 04:10 PM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902  What do you mean by this? That you do not know how to find $\displaystyle \nabla f$ or that you do not know how to use that to find $\displaystyle \nabla f\cdot \vec{v}$? For any function of two variables, f(x, y), $\displaystyle \nabla f= \frac{\partial f}{\partial x}\vec{i}+ \frac{\partial f}{\partial y}\vec{j}$. Here, $\displaystyle f(x, y)= 3x^2 y^2+ 4$ so $\displaystyle \nabla f= 6x\vec{i} 2y\vec{j}$. Evaluate that at x = 7, y = 5 and take the dot product of that with $\displaystyle 6\vec{i}+ 8\vec{j}$. Last edited by skipjack; March 3rd, 2017 at 05:16 PM. 
March 3rd, 2017, 03:16 PM  #5  
Newbie Joined: Feb 2017 From: Michigan Posts: 17 Thanks: 0  Quote:
Last edited by skipjack; March 3rd, 2017 at 05:16 PM.  
March 3rd, 2017, 05:24 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,934 Thanks: 2208 
I haven't checked your calculation, but your expression is equivalent to 22√5/5.


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