## 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 $$f$$.

.

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?