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First, we need to recall 2 basic definitions of vector operations: The dot product is defined on vectors u =[u 1 , u 2 ,...u n ] and v =[v 1 , v 2 ,..., v n ] as u . v = u 1 v 1 +u 2 v 2 +...+u n v n The len...

The chain rule is used when you're trying to differentiate a complicated function, and it allows you to split up the function into easier ones. The trick is spotting where to split the function, and what par...

So you've encountered something like: g(x) = | 4 f( |x + 1| - 3 ) + 5 | What a mess! And you are only given the graph of f(x). How do we go about sketching g(x)? As in any problem in mathematics, let's break...

I have A* in Maths and Further Maths at A-level, and have tutored students in A-level maths for a year.

A stationary point is simply a point on a graph where the derivative=0. Ie, the rate of change of the curve at this point is 0 and therefore it is neither increasing or decreasing at this point . There are t...