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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) - the derivative ...

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 solution...

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 squar...

Can re-write function as y=4x 1/2 Then 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 the power w...

Firstky differentiate to gain an equation for the gradient.Differentiating gives:dy/dx = 6x 2 Insert x = 2 into the above equation to find the gradient at that particular point of the curve.When x = 2, dy/dx...