# The function π(π₯)=2π₯^3β27π₯^2+108π₯β11 has two critical numbers.?

The smaller one equals(blank) and the larger one equals(blank)Β

### 1 Answer

Relevance

- L. E. GantLv 71 month agoFavorite Answer
critical values occur when the derivative of the function equals 0

so f'(x) = 6x^2 - 54x + 108 = 0

==>x^2 - 9x + 18 = 0

==> (x-3)(x-6) = 0

==> x = 3 or x = 6

in addition:

f"(x) = 12x - 54

f"(3) = 36 - 54 = - 18 ==> a maximum

f"(6) = 72 - 54 = 18 ==> a minimum

will leave it to you to find f(3) and f(6)

and work out the rest of the answer.

Still have questions? Get your answers by asking now.