Find the coordinates of the point on the curve $f(x)=3x^2-4x$ where the tangent is parallel to the line $y=8x$.

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    $\begingroup$ Any thoughts/attempts of your own? $\endgroup$ – Kaster Feb 9 '15 at 22:24
  • $\begingroup$ I can't figure it out $\endgroup$ – Serenade Feb 9 '15 at 22:25
  • $\begingroup$ Have you graphed the function and the line? What information does the derivative of a function give you about that function? How can we know two lines are parallel? $\endgroup$ – Bernard Massé Feb 9 '15 at 22:53
  • $\begingroup$ That's all I've been given in the question. I'm just a week into grade 12 calculus. $\endgroup$ – Serenade Feb 9 '15 at 22:55
  • $\begingroup$ You might get an answer here which will help you ace your homework, but when it comes to test time you will not be able to turn to the Internet. Best to bring your questions to your teacher. $\endgroup$ – Matthew Leingang Feb 9 '15 at 22:57

The derivative of the function $f$ tells you the slope of the tangent to $f$ at the point $(x, f(x))$. Since the tangent has to be parallel to the line $y = 8x$, it is clear that the slope must be $8$. Therefore, $$f'(x) = 8 \implies 6x - 4 = 8 \implies x = 2$$

The point is then $(2, 4)$.


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