Answer
A) $f'(-3) \approx -0.4$
B) $f'(-2) \approx 0$
C) $f'(-1) \approx 0.75$
D)$f'(0) \approx 1.5$
E) $f'(1) \approx 0.833$
F) $f'(2) \approx 0$
G $f'(3) \approx -0.5$
Work Step by Step
This question is asking you to estimate the value of the derivative at a given point. Since we know the derivative is equal to the slope of the tangent line, we can find the line tangent to the graph at the specified point, and determine its slope from the graph.
A) In order to find the slope of the tangent line, draw a line tangent to the point and draw a triangle down to see the difference in x and y, as seen on the attached graphs. For A, we can see that the change in the y direction (the rise) of the triangle is -2, and the change in the x direction (the run) is 5. Slope is $\frac{rise}{run}$, so we can see that the slope of the tangent line at this point is -0.4.
B-G) See Part (A) for detailed instructions as to how to find the slope of a tangent line, and reference the attached picture to see the specific graphs for each part. Note that for problems (B) and (F), the tangent line is flat, or has a slope of zero. This happens when the graph is at the bottom of a well or at the top of a peak.
