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By definition, turning points occur when the gradient function equals to zero. To prove this we need to differentiate the function given. To differentiate, bring the power down and multiply it by the co-e...

y = 3x^2 − (2/3) x + 1Derivative of 3x^2 = 6x3 * 2 = 6x^(2-1) = x^1 = xDerivative of -(2/3)x = -2/3-(2/3) * 1 = -2/3x^(1-1) = x^0 = 1dy/dx = 6x - 2/3at x = 0dy/dx = 6(0) - 2/3dy/dx = -2/3

Whenever you see fractions of x or x² etc top or bottom, your first port of call would have to be to convert them into partial fractions. Once you have done this, the questions you would get w...

Mathematics is a unique subject within which many equations that you encounter have lots of functions and can be derived from the basics. The quadratic formula for instance is incredibly useful to quickly...