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 off.) For each interval, enter all letters whose corresponding statements are true for that interval. The interval from a to b The interval from b to c The interval from c to d The interval from d to e 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

The given graph is f'(x) basically, the derivative

a to b :
Notice the graph exists in the negative y-side, i.e below
the x-axis and it is rising, as in increasing.
Since the derivative is negative, the original function decreasing here
It is decreasing but the derivative is increasing, so it is cnc up
So, option B,C,F,G

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b to c :
A,C,E
Increasing derivative and increasing function
So conc up
A,C,E,G

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c to d :
A,D,E
Decreasing derivative and increasing function
So, conc down
A,D,E,H

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d to e :
B,D,F
Decreasing derivative and decreading original function
So, conc down
B,D,F,H

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e to f :
B,C,F
Increasing derivative and decreasing original function
Conc up
B,C,F,G

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