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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...

First we have to find the first derivative of f(x), we do this using the quotient rule. Once we have obtained the first derivative, we know this gives us the rate of change of f(x), we can therefore say t...

loga12
explantion:from simples rules of logs