This problem has to do with the second derivative of a function. Here's the problem:
A function f has f(3) = 20, , and > 0 for x > 3. Which of the following are possible values for f(5)? State why or why not.
(Note: It's NOT multiple choice. It's asking you to consider each on of these values, say whether or not they would be possible values for f(5), and then explain why you said yes or no. Just to clarify...)
What I've Done So Far: I attempted to graph f(x), because I know that the point (3 , 20) is on it, and the tangent line to that point has a slope of 2. I also know the graph is increasing, and is concave up from , implying that before that point, it's concave down (...right?). Having graphed it...I'm lost. I have no idea how to determine whether or not these are possible values. My best guess was to base it off of the slope (being 2). According to my poorly drawn graph, it doesn't look like b or c would be possible because of how the graph is increasing. But it seems incorrect to just eyeball it like that.
Any help would be greatly appreciated!
a.) does that mean none of these values are possible?
b.) how do you figure that if f(x) is linear it would be 26? Is it because the slope at x = 3 is 2, so you're just going up 2 over 1 for x = 4 then x = 5?
Thank you for your reply! ....I'm still confused as to how I should answer this question though.
And no, it's not a web problem. Just a particularly confusing one on a homework assignment I have. It's not multiple choice either. It's saying that you have to consider each of those values, and say whether or not they would be possible, and why.