1. ## Slope Help?

f(x)-------x
31.25-----2.5
39.20-----2.8
45--------3.0
48.05-----3.1

The function f is differentiable and has values as shown in the table above. Both f and f ' are strictly increasing on the interval [0,5]. Which of the following could be the value of f ' (3)?

a. 20
b. 27.5
c. 29
d. 30
e. 30.5

I've already ruled out choice a and b, but between c, d, and e, I don't know which one is correct.

2. ## solved.... maybe

When I did a quadratic regression, and derived the formula, I got: $4.79\bar{54} x + 1.106\bar{81}$

so, once you put in 3, you get roughly $29.879\bar{54}$

So, I'd say it's D.

But to have a more clear answer, if you take the slope between points (3,45) and (2.8,39.2); you get 29.
Then with points (3.1,48.05) and (3,45); you get 30.5

Obviously then since the function is continuous, it must be in between 29 and 30.5, which gives option D.

hope this helps.