What can be determined if g(1) = -3, g'(1) = 0, and g"(1) = 2?

Question

anonymous · Answer

the point is $(1,-3)$ is a local ____...

we know that $g'=0$ which tells us it's potentially a local extremum, and $g''>0$ tells us it's curving upward at the point sorta like this:|dw:1389677209278:dw|

anonymous · Answer

local minimum

anonymous · Answer

very good :-)

anonymous · Answer

It makes more sense when you put it like that.

anonymous · Answer

I hope so! :-) the second derivative tells us how it bends around the point... if $g''>0$ it bends upward while if $g''<0$ then it bends downwards. similarly the first derivative tells us whether it's sloped upward ($g'>0$), downward ($g'<0$), or "flat" ($g'=0$). where a function is locally flat but curving upward we must be a local minimum while if a function is locally flat but curving downward then it's a local maximum since $g(1)=-3$ we know the point on the graph is $(1,g(1))=(1,-3)$