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f(x) = 3x^3 + 2x^2 - 8x + 4

f(2) = 3(2)^3 + 2(2)^2 - 8(2) + 4

f(2) = 3(8) + 2(4) - 8(2) + 4

f(2) = 24 + 8 - 16 +4

f(2) = 20

a) By simple parametric differentiation of each term, dy/dx = 2x^2 + 2x b) The condition for a turning point is the gradient (dy/dx) at that point is zero. 0 = x(2x + 2) so either x=0 or 2x+2=0. Therefore...

We integrate by parts: u=x   u'=1;  v'=sin(x)  v=-cos(x) integral(xsin(x)dx) = -xcos(x) + integral(cos(x)dx) = -x*cos(x) + sin(x) + C where C is a constant.

The general method for (a+b)^n is: 1)write out pascals triangle (see whiteboard) and stop at the nth row. Write this on a line. 2)write down the powers of a in ascending order (and simplify) 3)write down ...

A-Level Mathematics is about a wide range of topics, among which Integrating is key!

While differentiation is a technique, whereby a set of rules can be used to approach problems, integration is an...