The graph shown is the graph of the SLOPE of the tangent line of the original fu

Question

The graph shown is the graph of the SLOPE of the tangent line of the original function. (This slope is also called the derivative of f.)
For each interval, choose all letters whose corresponding statements are true for that interval.

1. The interval from a to b

2. The interval from b to c

3. The interval from c to d

4. The interval from d to e

5. The interval from e to f

A. The slope of the original function is positive on this interval
B. The slope of the original function is negative on this interval.
C. The slope of the original function is increasing on this interval.
D. The slope of the original function is decreasing on this interval.
E. The original function is increasing on this interval.
F. The original function is decreasing on this interval.
G. The shape of the original function is concave up on this interval.
H. The shape of the original function is concave down on this interval.

Explanation / Answer

1.
in interval a to b
B. The slope of the original function is negative on this interval.
C. The slope of the original function is increasing on this interval.
F. The original function is decreasing on this interval.
G. The shape of the original function is concave up on this interval.

2.
in interval b to c
A. The slope of the original function is positive on this interval
C. The slope of the original function is increasing on this interval.
D. The slope of the original function is decreasing on this interval.
E. The original function is increasing on this interval.
G. The shape of the original function is concave up on this interval.
H. The shape of the original function is concave down on this interval.

3.
in interval c to d
A. The slope of the original function is positive on this interval .
D. The slope of the original function is decreasing on this interval.
E. The original function is increasing on this interval. .
H. The shape of the original function is concave down on this interval.

4.
in interval d to e
B. The slope of the original function is negative on this interval.
C. The slope of the original function is increasing on this interval.
F. The original function is decreasing on this interval.
G. The shape of the original function is concave up on this interval.

5.
in interval e to f
B. The slope of the original function is negative on this interval.
C. The slope of the original function is increasing on this interval.
F. The original function is decreasing on this interval.
G. The shape of the original function is concave up on this interval.

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