concavity and derivatives

Question

Let 𝑓 be a twice differentiable function on an open interval (𝑎,𝑏).

Which statements regarding the second derivative and concavity are true?

a)If 𝑓″(𝑐) is positive, then the graph of 𝑓 has a local maximum at 𝑥=𝑐.

b)The graph of 𝑓 has a local minimum at 𝑥=𝑐 if 𝑓″(𝑐)=0.

c)The concavity of a graph changes at an inflection point.

e)If 𝑓 is increasing, then the graph of 𝑓 is concave down.

d)The graph of 𝑓 is concave up if 𝑓″ is positive on (𝑎,𝑏).

Answer 1