Question

For what value of x does the function f(x)=x³-9x²-120x+6 have a local minimum?

Answer 1

f(x) = x³ - 9x² - 120x + 6

f'(x) = 3x² - 27x - 120 = 0

x² - 9x - 40 = 0

x = (9 ± √((-9)² - 4(1)(-40)))/2

= (9 ± √(81 + 160))/2

= (9 ± √241)/2