Question

Show that the function f(x)=x3-3x2+6x-100 is increasing on r

Answer 1

your answer for above question

Answer 2

Hey !!

f(x) = x³ - 3x² + 6x - 100

f'(x) = 3x² - 6x + 6

       = 3(x² - 2x + 2)

Discriminant of the formed quadratic = b² - 4ac

          = (-2)² - 4(1)(2)

          = 4 - 8

           = -4

b² - 4ac < 0

      but a > 0         [ a = 1 ]

Hence, x² - 2x + 2 > 0           for all x ∈ R

        ∴    3 (x² - 2x +2)   ;         x ∈ R

       f'(x)     > 0                ;           x ∈ R

Hence f(x) is increasing on R

Good luck !!