Answer:
steps below
Step-by-step explanation:
f(x) = 5x³ - x² - 5x + 1
Local extremes: 15x²-2x-5=0 .. gradient=0
x = (2 ± √2²-4*(15)*(-5)) / (2*15)
= (2 ± √304) / 30
= (2 ± 4√19) / 30
= (1 ± 2√19) / 15
= (1 ± 8.718) / 15
local maximum: (1 + 8.718) / 15 = 0.648
local minimum: (1 - 8.718) / 15 = - 0.515
the interval(s) where the graph is increasing: x < - 0.515 or x > 0.648
the interval(s) where the graph is decreasing: - 0.515 < x < 0.648
