Answer
B
Work Step by Step
The slope of the tangent line through the point on the graph of $f$ where $x=a$ is given by the instantaneous rate of change, or derivative
$m_{tan}=$ slope of tangent $=$ instantaneous rate of change$=$derivative $=f^{\prime}(a)$
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1. The tangent slope is positive at x=0, (the graph is rising).
2. From x=0 to x=4, as we slide right tracing the graph,
the slope gradually becomes less and less steep (still positive though),
until it becomes momentarily 0 at x=2.
So, from x=0 to x=2, the slope decreases.
3. Then, continuing to trace the graph to the right,
from x=2 (slope 0) onwards to x=4,
the tangents get gradually steeper and steeper
(the slopes are positive and increasing).
This is best described by choice B.
