A specialized hydraulic piston's displacement DDD (in mm) relative to a benchmark is modeled by the equation:
D(t)=25∣5t+8∣−6,t∈RD(t) = \frac{2}{5}|5t + 8| - 6, \quad t \in \mathbb{R}D(t)=52∣5t+8∣−6,t∈R
where t t\,t is the time in seconds.
State the coordinates of the vertex, VVV, of the graph of y=D(t)y = D(t)y=D(t).
Using algebra, determine the set of values of t t\,t for which D(t)>2−15tD(t) > 2 - \frac{1}{5}tD(t)>2−51t
Sketch the graph with equation y=∣D(t)∣y = |D(t)|y=∣D(t)∣, stating the coordinates of the local maximum point and each local minimum point.