Consider the function
f ( x ) = − 2 x 3 + 42 x 2 − 240 x + 9 \displaystyle {f{{\left({x}\right)}}}=-{2}{x}^{{3}}+{42}{x}^{{2}}-{240}{x}+{9} f ( x ) = − 2 x 3 + 42 x 2 − 240 x + 9 .
For this function there are three important open intervals:
( − ∞ , A ) \displaystyle {\left(-\infty,{A}\right)} ( − ∞ , A ) ,
( A , B ) \displaystyle {\left({A},{B}\right)} ( A , B ) , and
( B , ∞ ) \displaystyle {\left({B},\infty\right)} ( B , ∞ ) where
A \displaystyle {A} A and
B \displaystyle {B} B are the critical numbers.
Find
A \displaystyle {A} A Preview Question 6 Part 1 of 5
and
B \displaystyle {B} B Preview Question 6 Part 2 of 5
For each of the following open intervals, tell whether
f ( x ) \displaystyle {f{{\left({x}\right)}}} f ( x )
is increasing or decreasing.
( − ∞ , A ) \displaystyle {\left(-\infty,{A}\right)} ( − ∞ , A ) :
Select an answer
Increasing
Decreasing
( A , B ) \displaystyle {\left({A},{B}\right)} ( A , B ) :
Select an answer
Increasing
Decreasing
( B , ∞ ) \displaystyle {\left({B},\infty\right)} ( B , ∞ ) :
Select an answer
Increasing
Decreasing
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Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)