How do you determine whether the function

Mary Bates

Mary Bates

Answered question

2022-04-16

How do you determine whether the function f(x)=x46x3 is concave up or concave down and its intervals?

Answer & Explanation

Wrastirtyzp9w

Wrastirtyzp9w

Beginner2022-04-17Added 10 answers

Step 1
f(x)=x46x3
f(x)=4x318x2
f (x)=12x236x=12x(x3)
f (x)=0 at 0 and at 3
Step 2
On (,0), we have fx)>0 so the graph of f is concave up.
On (0, 3), we have fx)<0 so the graph of f is concave down.
On (3,), we have fx)>0 so the graph of f is concave up.
Inflection points are (0, 0) and (3,81).

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