How do you determine whether the function

Miguel Hanson

Miguel Hanson

Answered question

2022-04-15

How do you determine whether the function f(x)=3x24 is concave up or concave down and its intervals?

Answer & Explanation

wyjadaczeqa8

wyjadaczeqa8

Beginner2022-04-16Added 14 answers

Step 1
f(x)=6x(x24)2 Critical points are that at which f(x)=0 or where it does not exist. These in this case are -2,0,2. Hence the interval to be tested are
(, 2), (2, 0), (0, 2) and (2, )
For using second derivative test, f(x)=63x2+4(x24)3
Select any test value in these intervals and test for the sign of fx).
In (, 2) it would be >0, conclusion, concave up
In (2, 0), it would be <0,   , concave down
In (0, 2) it would be <0,   , concave down
In (2, ), it would be >0   , concave up

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