Question

F(x)=2x^3-9x^2+12x-3 find the intervals on which f is increasing or decreasing

Answer 1

f'(x) = 6x^2 - 18x + 12

= 6(x^2 - 3x + 2)

= 6(x - 2)(x - 1) = 0   at turning points
at turning points  x = 1 and x = 2

f''(x) = 12x - 18  

so when x = 1 f''(x) <0  (maximum) and  when x = 2  f''(x) > 0 (minimum)