Answer:
- f'(2) = 0
- f'(4) = 1/2
- f'(7) = 0
Step-by-step explanation:
The derivative at a point is the slope of the graph at that point.
a = 2
The line is horizontal at x=2, so the slope is zero.
f'(2) = 0
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a = 4
The graph at that point is on a linear portion of the curve. The line has a rise of 1 for a run of 2, so the slope is ...
f'(4) = rise/run = 1/2
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a = 7
The curve has a maximum at x=7, so the derivative of the function there is zero. (Extrema occur where the derivative is zero.)
f'(7) = 0
