Provide an appropriate response.Explain why the following four statements ask for the same information.(i) Find the roots of f(x) = 3x3 - 3x - 1(ii) Find the x-coordinates of the intersections of the curve y = x3 with the line y = 3x + 1.(iii) Find the x-coordinates of the points where the curve y = x3 - 3x crosses the horizontal line .(iv) Find the values of x where the derivative of g(x) = x4 - x2 - x + 5 equals zero.

Question

What will be an ideal response?

Answer 1

(i) The roots of the function y = 3x³ - 3x - 1 can be calculated by using Newton's method. Resulting in three roots: -0.743275, -0.39485248, and 1.13725448.

(ii) The x-coordinate of the intersection of y = x³ and y= 3x + 1 is the root of  

(iii) The curve y = x³ - 3x crosses the horizontal line y = 1 at the solution of  which is the same as the functions in part (i) and (ii).

(iv) The values of x where the derivative of g(x) equals zero are the same as the functions in part (i) and (ii)