Question

What is the differnce between where a function increases (first derivative test) and finding concavity( second derivative test), does the first derivative test tell us if the function is increasing or decreasing??

Answer 1

but why do we need to know convaity, if the first derivative test tells us whether the function is increasing or deacresing

Answer 2

because a function can be increasing, but have a concavity of either up or down, the same goes for a decreasing function; so you can't draw a graph unless you know both

Answer 3

thank you