How do you know where the graph of

Destinee Bryan

Destinee Bryan

Answered question

2022-04-10

How do you know where the graph of f(x) is concave up and where it is concave down for f(x)=x3+x?

Answer & Explanation

Drantumcem0

Drantumcem0

Beginner2022-04-11Added 10 answers

The graph of f is concave up on intervals on which f''(x) is positive and the graph is concave down where f''(x) is negative.
Explanation:
So we need to investigate the sign of f"(x).
f(x)=x3+x
f(x)=3x2+1
fx)=6x
Clearly, fx)=6x is negative for x<0 and positive for x>0.
So the graph of f is concave down on (,0) and it is concave up on (0,).

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