steps to use derivatives to graph

find f'/critical points, find where f is increasing, find f"/inflection points where f"=0/concavity, check for asymptotes/intercepts

first derivative of position function

second derivative of position function

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MATH 155- Quiz 7

Question	Answer
f'(x) <0	function is decreasing
f'(x) >0	function is increasing
f"(x)<0	concave down
f"(x)>0	concave up
steps to use derivatives to graph	find f'/critical points, find where f is increasing, find f"/inflection points where f"=0/concavity, check for asymptotes/intercepts
velocity	first derivative of position function
acceleration	second derivative of position function
f(x)=e^ax derivative and 2nd derivative	f'(x)=ae^(ax) f"(x)=a^2e(ax)