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First, we must find the value of x that corresponds to the stationary point, i.e. where the gradient (dy/dx) is zero. This will be in terms of 'a' (if we change 'a,' we change the shape of the function by...

We first notice it's a quadratic equation in x so we want to make one side of the equation equal to 0.By adding 15 to both sides we get : x² + 8x + 15 = 0We then look for two numbers which mul...

First draw out the free body diagram for the problem, marking on all forces acting on the objects ie. the mass of the block and the reaction force normal to the plane and the forces acting due to friction...

Setting (1 + kx)ⁿ equal to 1 - 6x + 30x² + ..., the binomial expansion can be applied to the LHS, by making use of the formula provided in the formula book. In this case, where x app...

Completing the square is a method for rewriting a quadratic expression, and can be useful in identifying the minimum value of the expression. The aim is to end up with an expression which looks like c((x+...