Question

The function f is continuous on the interval [3, 13] with selected values of x and f(x) given in the table below. Use the data in the table to approximate f '(3.5)

x 3 4 7 10 13
f(x) 2 8 10 12 22

Answer 1

The function is clearly not linear, so I'd just go with the slope of the segment from f(3) to f(4).
That would make f(3.5) = (2+8)/2 = 5

Plotting the points makes the graph look like a cubic with the greatest curvature near (7,10) so our approximation should be fairly close.

Answer 2

I think what you're supposed to do is find the point between three and four since it is f(3.5).
This means you would do slope formula, which is (8-2)/(4-3), and you would get 6.

Answer 3

Yes you are correct - 6 is the answer!