Let f(x)=x^3-6x+3. i)Differentiate f(x) to find dy/dx. ii) Given that dy/dx = 12, find the value of x.

For part i) we use the basic method of differentiation by considering each term individually. The first term, x³ goes to 3x² by multiplying the original term by the original power, by 3, and then subtracting 1 from the original power. The second term goes to -6 as by differentiation when x is to the power 1 it disappears. The constant term 3 disappears as there is no x term to differentiate. This gives the answer, dy/dx =3x²-6. For part ii)  equate the answer to i) to the given value, i.e. 3x²-6=12. This simplifies to 3x²=18 by adding 6 to both sides and then again to x²=6 by dividing by 3. To get the value of x, take the square root of both sides, x=+sqrt(6) or x=-sqrt(6). You get two answers due to the nature of taking a sqaure root.