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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 ).
S...

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...

Can re-write function as y=4x^1/2Then follow the standard steps for differentiating a power. Take the 1/2 down and multiply by the number in front of the x, in this case 4, to give 2. Now reduce...