Let $y = f(x)$ for -0.5 less than or equal to $x$ less than or equal to 6.5.

Let $ y = f(x)$ for -0.5 less than or equal to $ x$ less than or equal to 6.5.

The following diagram shows the graph of $ f’$ , the derivative of $ f$ .

diagram here.

a) Explain why the graph of $ f$ has a local minimum when $ x=5$ .

b) Find the set of values of $ x$ for which the graph of $ f$ is concave down.

for part a, i’m very confused because $ x=5$ doesn’t even look like a minimum. wouldn’t it be $ x=4$ ??

for part b, would it just be $ x=2$ because that’s when the graph looks concave down?