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2. Intro to Derivatives
2. Intro to Derivatives / Tangent Lines and Derivatives / Problem 2
Problem 2

A rocket is launched vertically up, and its height above the ground is given by the function h(t)=400t50t2h\(\left\)(t\(\right\))=400t-50t^2, where hh is in meters and tt is in seconds. The graph below shows h(t)h\(\left\)(t\(\right\)) along with its velocity function v(t)=dhdtv\(\left\)(t\(\right\))=\(\frac{dh}{dt}\) and the acceleration function a(t)=d2hdt2a\(\left\)(t\(\right\))=\(\frac{d^2h}{dt^2}\) for the time interval 0t80\(\le\) t\(\le\)8 s\(\text{s}\).

Using the graph, determine the time when the rocket changes direction.