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

f'(12)= 5

Step-by-step explanation:

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

 x3471113

f(x)28101222

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 =

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

f'(12) =

so f'(12)= 5

First do 3/2⁻⁷, which equals to (2/3)⁷ , which equals to 128/2187.

Then do (2x⁻¹)⁻⁵, which is x⁵/2⁵ = x⁵/32.

Multiply the two and the answer is:

128/2187*x⁵/32

= 4/2187 * x⁵

Hope this helped. : )