Answer:
minimum point is (3, -25) and maximum point is (-1, 7)
Explanation:
f(x) = x³ - 3x² - 9x + 2
Differentiate:
f'(x) = 3x² - 6x - 9
Equal f'(x) to zero and solve to find values of x:
f'(x) = 0
3x² - 6x - 9 = 0
(x - 3)(x + 1) = 0
x = 3, -1
Plug in values of x into original function to find coordinates of turning/stationary points: (3, -25) and (-1, 7)
Differentiate again:
f''(x) = 6x - 6
Plug in x value of stationary points to find nature of point:
f''(3) = 6(3) - 6 = 12 > 0 ⇒ minimum
f''(-1) = 6(3) - 6 = -12 < 0 ⇒ maximum
Therefore, the minimum point is (3, -25) and maximum point is (-1, 7)