How do you determine whether the function

Ramiro Grant

Ramiro Grant

Answered question

2022-04-17

How do you determine whether the function g(x)=x2+3x+4 is concave up or concave down?

Answer & Explanation

cab65699m

cab65699m

Beginner2022-04-18Added 14 answers

Answer:
Using calculus, to determine concavity, investigate the sign of the second derivative.
g(x)=x2+3x+4
g(x)=2x+3
gx)=2
Since g"(x) is always negative, the graph of g is concave down on the domain of g. Which is to say: g is concave down on (,).
Using algebra, the graph of this quadratic is a parabola. Since the coefficient of x2 is negative, the parabola opens downward. It is concave down.

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