How do you determine whether the function

Terrence Riddle

Terrence Riddle

Answered question

2022-04-15

How do you determine whether the function f(x)=2x3+3x2432x is concave up or concave down and its intervals?

Answer & Explanation

Gonarsu2dw8

Gonarsu2dw8

Beginner2022-04-16Added 19 answers

Answer: f(x) is concave down on (;12) and concave up on (12;)
Step 1
You have to investigate the sign of the second derivative around its zero points (inflection points).
In this case,
f(x)=6x2+6x432
f(x)=12x+6
Step 2
fx)=0x=12
x<12fx)<0 and hence the concavity is down.
x12fx)>0 and hence the concavity is up.

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