homework - functions

Question

The function f ( x ) = − 2 x 3 − 15.84 x 2 + 125.4528 x − 2.93 is increasing on the open interval ( , ).

It is decreasing on the open interval ( − ∞ , )

and the open interval ( , ∞ ).

The function has a local maximum at .

Answer 1

f ( x ) = − 2 x 3 − 15.84 x 2 + 125.4528 x − 2.93

f'(x) = -6x² - 31.68x+ 125.4528 =

-6/625/(625x² + 3300x - 13068) =

-66/25(25x - 66)(25x + 198)

x = 66/25,-198/25

The function is decreasing on (-∞, -198/25) and (66/25, ∞) It increases on (-198/25, 66/25)

It has a local maximum at 66/25 y = 181.0674

(2.64,181.0674)