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In order to find the equation of the tangent line, first we have to find its slope. To do this, we take the first derivative of the function. In this particular case, we just need to apply the power rule ...

Firstly, we need to recognise that the question stated that the quadratic equation has equal roots. This tells us that the discriminant of the equation (b^2 - 4ac) will be an important pa...

There is always a systematic approach to answering questions that require you to complete the square. Before you start answering the question make sure the coefficient of x^2 is 1. For th...

First complete the square on the curve in the answer to obtain y=(x+2)² - 5 Now if you were to call your original equation y=f(x) you could see that the new equation is simply y=f(x+2) - 5This ...

Here we need to use the product rule in order to differentiate as we have two functions involved that are being multiplied together. Therefore we use the formula:dy/dx = u dv/dx + v du/dxFirst let u=(x^2 ...