Question

f(x) = 2 x^3 - 24 x^2 + 90 x + 14 is increasing.

Answer 1

f ' (x) = 6x^2 - 48x + 90

set this equal to zero for "turning points"
x^2 - 8x + 15 = 0
(x-5)(x-3) = 0

so turning points when x = 3 and when x=5
the curve is rising for x>5 and it is rising for x<3
(it is decreasing between 3 and 5)

I will let you write it in the notation that you learned.