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I have one more similar ACT question. I asked you one before, about the Chain Rule; this is similar, but I'm not sure on how to apply that rule to finding the tangent line. I follow the process in the workbook, but keep getting different answers. Hoping you could help. Thanks.

It is:

Write an equation of the tangent line to the curve of y=(4x^(2)-2x)^3 at x=1

Hi John,

It would be more helpful if you showed me your progress. Anyway, following the same manner as before;

y = (4x² - 2x)³

Let u = 4x² - 2x

then

y = u³ and dy/du = 3u²

du/dx = 8x - 2

dy/dx = (dy/du).(du/dx)

= 3u² . (8x - 2)

= 3(4x² - 2x)² . (8x - 2)

and at x = 1,

y = 8

dy/dx = 72 (which would be the slope of the tangent line at that point (1,8))

The equation is then, using the cartesian co-ordinates formula;

(y-8)/(x-1) = 72

y - 8 = 72(x - 1)

y - 8 = 72x - 72

y = 72x - 64

Regards

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