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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
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 Originally Posted by Prove It 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*}?
No, I don't.

Last edited by skipjack; March 3rd, 2017 at 04:36 PM. March 1st, 2017, 04:10 PM   #4
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 Originally Posted by b19 No, I don't.
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
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 Originally Posted by Country Boy 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 $\displaystyle 6\vec{i}+ 8\vec{j}$.
Ok, I know my answer is = -12/sqrt20(7) - -8/sqrt20 (5) so my answer in decimal form is -9.84 ... but I need my answer to be in a form for example -66 sqrt2/5, can someone convert that for me because I don't know how to... thanks.

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. Tags answer Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post theturk Algebra 1 January 25th, 2014 05:21 PM rage Algebra 2 September 14th, 2012 09:27 PM RealMadrid Algebra 2 April 17th, 2012 01:26 PM mimi Linear Algebra 2 November 30th, 2009 09:43 AM honestliar Calculus 2 November 24th, 2009 09:18 AM

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