Need Help with First/Second/Third Derivative relation

[tangents]

Hello all,

Well I am kind of stumped on this question and was hopeing for somr guidance.

X 1.1 1.2 1.3 1.4
f(x) 4.18 4.38 4.56 4.73

F is obviously a function and f ''(x)<o for all x in the closed interval. The question asks which of the following has to be for f '(1.2)?

1) f '(1.2)<0 This can't be it because f(x) is positive
2) 0<f '(1.2)<1.6
3) 1.6<f '(1.2) <1.8
4) 1.8< f '(1.2) <2.0
5) f '(1.2)> 2.0 This one is saying that the slope at 1.2 is greater than 2, but i suppose the only way to be certain is to graph the points and find out.As for the rest I'm not entirely sure but hope you guys can assist me ; ;

 

[dicerandom]

1) f '(1.2)<0 This can't be it because f(x) is positive

The reason you stated does not guarantee that the first derivative is positive. A positive valued function can have a negative slope and thus a negative first derivative.

5) f '(1.2)> 2.0 This one is saying that the slope at 1.2 is greater than 2, but i suppose the only way to be certain is to graph the points and find out.

You could graph them, or you could use rise over run.

I believe the problem intends for you to calculate the slopes of each of the lne segments connecting the points given in the problem and using those values to determine limiting values for the derivative at the indicated point.