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So I'm having trouble trying to solve this. I have been puzzling over it. I know I need to use the slope of the parallel line to find the derivative but I just can't seem to work it out in my head. I need to find the equation of the tangent line of: $$f(x)=−4x^2+11x−2 $$ at $$x=2$$ that is parallel to $$ y=-5x-1$$

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Firstly, we find the derivative to be $f'(x)=-8x+11$. At the point $x=2$, the derivative is equal to $-5$ (found by evaluating the derivative at this point), which tells us the slope of the tangent line. Since this and the slope of the given line are the same, then we just have to find an equation for this line. At $x=2$, the y-value of the function is $4$. Since we know the slope and a point, we can find the equation of the line to be $(y-4)=-5(x-2)$.

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  • $\begingroup$ $-44$? $-4*2^2+11*2-2=-16+22-2=-4$ $\endgroup$
    – Andrei
    Commented Sep 16, 2017 at 20:37
  • $\begingroup$ My bad, silly calculation error. I believe it is positive 4 though, I will fix now. $\endgroup$
    – Tyler6
    Commented Sep 16, 2017 at 20:39
  • $\begingroup$ Do you even need to find the derivative? It gives you the slope already and a coordinate point of the line we want. Just seems unnecessary to mention. $\endgroup$
    – green frog
    Commented Sep 16, 2017 at 20:52
  • $\begingroup$ If you assume the slopes are going to be equal no, I just did it to confirm that the slopes are indeed parallel. $\endgroup$
    – Tyler6
    Commented Sep 16, 2017 at 23:09

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