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Water is flowing into a tank. The function $d(v)$ gives the depth of the water in meters when the volume of the water in the tank is $v$ cubic meters. It turns out that $d'(10)=2$. Which statement best explains the meaning of $d'(10)=2$.
The images below show the graph of a parabola given by $y = f(x)$. To the right is an image zoomed in on the point $(3,f(3))$. It turns out that $f'(3)=0.75$. After zooming enough to where the graph of $f$ appears essentially linear, which statement best describes the length of the blue vertical vector?
The length of the blue vector is $0.75$. The length of the blue vector is $3$. The length of the blue vector is $f(3)$. The length of the blue vector is $0.75$ times as much as the value of $\Delta x$. The length of the blue vector is $0.75$ times as much as the value of $3$. The length of the blue vector is $0.75$ times as much as the value of $f(3)$.