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For a curve of f(x) against x, we can take the general point (x, f(x)) on the curve. By moving horizontally along the x-axis a distance of h, we also have the point (x+h, f(x+h)) on the curve. The gradient o...

A stationary point is where the curve has 0 gradient. So to prove that x=4 is a stationary point, we must find the equation of the first derivative. To do this, differentiate x 2 - 2x - 24sqrtx. It might hel...

Initially we find the first derivative of the function y = x 6 + sqrt(x). We achieve this by multiplying each x term by the power it is raised to, then reducing the power by 1 . Solution: 1) It helps to init...

Well in a binomial expansion we need to remember the formula (1+x)^n = 1 + nx + (n(n-1)(x^2))/2! + (n(n-1)(n-2)x^3)/3! + ... (I can draw this out properly on the whiteboard app)There is another formula but t...

A good way to approach this question is to first expand the brackets . This gives 12x 2 - 21x + 20x - 35 (remember to take the negative seven into account). We can then simplify this to give 12x 2 - x - 35 ....