Question

4 A curve has equation y=x^3 - 2x² +5. Find the coordinates of its two stationary points.​

Answer 1

Stationary points are (0, 5) and (4/3, 103/27)

Explanation:

At stationary point (turning point), dy/dx :

`y = {x}^(3) - 2 {x}^(2) + 5 \\ (dy)/(dx) = 3 {x}^(2) - 4x \\ \\ (dy)/(dx) = x(3x - 4)`

but dy/dx = 0:

`x(3x - 4) = 0 \\ either \: x \: is \: 0 \: and \: (3x - 4) = 0 \\ x = 0 \\ and \\ 3x - 4 = 0 \\ x = (4)/(3)`

let y = x³ - 2x² + 5:

`when \: x \: is \: 0 \\ y = 5 \\ when \: x \: is \: (4)/(3) \\ \\ y = {( (4)/(3)) }^(3) - 2 {( (4)/(3) )}^(2) + 5 \\ \\ y = (103)/(27)`