Question

WILL MARK BRAINIEST!!!!!! Given: f(x) = 5x3 - x2 - 5x + 1

Answer 1

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