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The curve's equation is presented as an implicit function. Therefore we must use implicit differentiation to solve this problem. To do this, we differentiate both sides of the equation with respect to x, ...

a) To show (x+2) is a factor, we want to show f(-2)=0. So (-2)^3-2(-2)^2 -29(-2)-42=-8-8+58-42=0
b) Divide  x^3 -2x^2-29x-42 by x+2 to get x^2-4x-21 which we factorise to get (x+3)(x-7). Hence f(x)=(...

This question is suited to A2 maths students, particularly those who are doing further maths and may be looking for a challenge. In one question it tests the students ability to use implicit differentiati...

loga12
explantion:from simples rules of logs

For this I would use the whiteboard to draw an even function (i.e cos(x)) and show that if f(x) is even then f(x) = f(-x). I would also show that the function would be symmetrical about the y axis. For an...