Question

1. 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 ′(12). (4 points) x 3 4 7 11 13

f(x) 2 8 10 12 22

Answer 1

5

Explanation:

I just took this and the answer calculated above is correct

Answer 2

f'(12)= 5

Explanation:

Use the data in the table to approximate f ′(12).

x 3 4 7 11 13

f(x) 2 8 10 12 22

f'(12) is nothing but the slope at x=12

To find slope at x=12 we two points from the table x=11 and x=13

(11,12) and (13,22)

Slope formula =
`(y2-y1)/(x2-x1)`

(11,12) is (x1,y1) and (13,22) is (x2,y2)

f'(12) =
`(22-12)/(13-11)=(10)/(2)= 5`

so f'(12)= 5