How do you determine whether the function

Gustavo Lam

Gustavo Lam

Answered question

2022-04-16

How do you determine whether the function f(x)=3x520x3 is concave up or concave down and its intervals?

Answer & Explanation

rhyclelal80j6

rhyclelal80j6

Beginner2022-04-17Added 13 answers

Step 1
For concavity we use the second derivative test.
f(x)=15x460x2
f(x)=60x3120x=60x(x22)
This second derivative equals zero if x=0 or x=2 or x=2
These are then the possible inflection points of the function where concavity could change.
We now investigate the sign of the second derivative around these points :
f is concave down on (; 2)(0; 2) and concave up on (2 0)(2; )

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