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To determine the characteristics of a graph, we need to examine what we are been shown in the question. Below is an exam style question:By looking at both the graph and the equation, we can see that in th...

y = e^x is an interesting function because for any value of x, the corresponding value of y is always equal to the gradient of the curve at that point.Therefore, f(x) is equivalent to f'(x) - th...

We must choose something to multiply the numerator and denominator of the fraction by the same thing, and the best thing to choose is the difference of two squares (since (x^2-y)(x^2+y)=x^2-y^2 ).
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Think about it as 'What numbers can be x to get 4'. Remember that when you square a number the answer is always positive? Here is a situation in which it's important to consider both of the possible solut...

Usually, there are two ways to solve this kind of problems. You could re-arrange the polynomial, make it become a square plus a constant, then the polynomial is greater or equal to the constant since a sq...