Derivative exam question: The problem is f'(x)>0 and f''(x)<0.

[WVteacher]

I am having trouble understanding the concept of derivative functions as graphs. How you know the equation of the graph if it is the derivative.

The problem is f'(x)>0 and f''(x)<0. When is it increasing/decreasing and is it concave up or down?

 

[Deleted member 4993]

I am having trouble understanding the concept of derivative functions as graphs. How you know the equation of the graph if it is the derivative.

The problem is f'(x)>0 and f''(x)<0. When is it increasing/decreasing and is it concave up or down?

You have put up bunch of questions (~5) - without showing single line of work!

What are your thoughts?

Please share your work with us ...even if you know it is wrong

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[WVteacher]

My thoughts

They give us f'(x)>0 which means increasing. Then f''(x)<0 which means concave down. Is this correct?

 

[stapel]

I am having trouble understanding the concept of derivative functions as graphs. How you know the equation of the graph if it is the derivative.

When you study calculus, you'll learn that there are infinitely-many functions which can have the same derivative function, so it is not possible to recover "the" function from the graph of the derivative. That said, they'll teach you loads about the relationship between a function and its derivative. (If you've taking algebra at all, the derivative is kind of the "slope", but for curvy graphs, too.)

The problem is f'(x)>0 and f''(x)<0. When is it increasing/decreasing and is it concave up or down?

I'm guessing you're using somebody else's account to post this question, since of course an instructor ("WVteacher") would know to provide more clear information. In this case, it is doubtful that "the problem" (the complete statement, plus instructions) "is f'(x) > 0 and f"(x) < 0".

Please reply with the full and exact statement of the exercise, the complete instructions, and a clear statement of your thoughts and efforts so far. For instance, since you appear (from other questions posted) to be studying algebra, how did you come to be assigned this calculus question? And so forth.

Thank you!