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f(x)=(12x^2)(e^2x) - 14, so using the chain rule f'(x)=(24x)(e^2x) + (12x^2)(2e^2x).To find the turning points set f'(x)=0, so (24x)(e^2x) + (24x^2)(e^2x) = 0. Thus (24xe^2x)(1+x)=0. Thus x=0 or x=-1.

Let's label the equations x² + y² = 25 (1) y - x = 1 (2). We can use substitution to solve this simultaneous equation. Let's make y the subject of the equation (2) and we get y = x...

To rationalise a surd means to manipulate a fraction involving terms which are being square rooted so that no term in the denominator is being square rooted. For this example 2/root(x) we multiply the fra...

Firstly, you need to get the equation to equal zero, so that you can use the quadratic formula to solve. Therefore you subtract 7 from both sides, meaning the equation becomes: 3x^2+7x-20=0. Recall the qu...