Let f and g be functions such that f prime (x) and g prime (x) are both continuous and increasing
for all real numbers x. Which of the following is ALWAYS true?

I. f + g is concave up everywhere.
II. f - g is concave up everywhere.
III. f multiplied by g is concave up everywhere.

Question

Let f and g be functions such that f prime (x) and g prime (x) are both continuous and increasing
for all real numbers x. Which of the following is ALWAYS true?


I. f + g is concave up everywhere.
II. f - g is concave up everywhere.
III. f multiplied by g is concave up everywhere.

dumbcow · Answer

well if slope is always increasing then function is concave up.

by multiplying functions, the degree changes so concavity may change
by subtracting functions, the degree may change so concavity may change
by adding functions, degree always stays same, thus concavity does not change

therefore f+g is Always concave everywhere

dumbcow · Answer

*concave up

dumbcow · Answer

wow this is from like a month ago...it may be time to close it :)

anonymous · Answer

Hello there, some of my classmates quesiton me why the answer would be such as you explained. I was not able to explain. I am looking for more explanations. :)