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Calculus on Steroids – Differentiation from Scratch!


Don’t worry – nobody will worry too much if you can’t follow this diagram and working. It’s here for the geeks, and those who really have to know WHY differentiation works. What do we mean by Differentiation? Simply, how to find the gradient of that straight line at any point on the curve. (It does have deeper meaning but this keeps it simple for now). So, ignore this little post if you like and wait for the next one that shows you the simplicity of Differentiation!

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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