FUNTIONS f(t) = 2w^3-33w^2+180w+11

Question

The function  f(t) = 2w^3-33w^2+180w+11 has one local minimum and one local max. 

This function has a local minimum at x = ? with the value ?

and a local maximum at x equals ? with value ?

Answer 1

f(w) = 2w³ - 33w² + 180w + 11

 

f'(w) = 6w² - 66w + 180 = 0

 

              w² - 11w + 30 = 0

 

              (w - 6)(w - 5) = 0

 

The critical values of f are w = 6 and w = 5

 

 

            +           l      -       l      +       sign f'

                         5            6

 

The derivative changes sign from + to - at x = 5.  So, there is a relative max at the point (5, f(5)) = (5, 336).

 

The derivative changes sign from - to + at x = 6.  So, there is a relative minimum at the point (6, f(6)) = (6, 335).