Question

If f’ is decreasing, what conclusion can be made about f?
A. f is positive
B. f is negative
C. f is concave up
D. f is concave down

Answer 1

D - f is concave down

Answer 2

thats what i was thinking... textbook=no help lol..

Answer 3

wait actually i though it would be concave up? if it is decreasing... \

Answer 4

I'm trying to come up with a good reason to explain it but i just had a quiz on this and f' is the rate of change so if it is decreasing that shows that f is going up, but also down, because it depends when f' crosses the x-axis

Answer 5

when f' is decreasing and crosses the axis that shows a maxima which is why the curve is concave down

Answer 6

Thank you. So one is to assume it crosses the x axis? And my friend argued with me earlier that it was B. Your thoughts on this?

Answer 7

Let me go back through my notes, I'm almost sure of this

Answer 8

Be careful... just because the first derivative is decreasing, does not mean it will cross the x-axis. The only thing you can pull from this info is that f is concave down.

Answer 9

they don't give you any info about f' such as f'<0 or f'>0? because technically you can say both depending on where f' is on the graph...

Answer 10

Good! Then I was correct assuming from the info given in the question.

Answer 11

Thanks @ByteMe and @sjerman1