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. 

Answered by Samuel H. Maths tutor

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