What is the difference between the approximation and the actual value of f′(0.5)?

Difference between the approximation and the actual value of f′(0.5) is 0.4330

Step-by-step explanation:

As complete question is not give, so considering the most relevant  question to given statement in Fig below.

from table

x        0       1      

f(x)      1       2

f'(0.5)=?

from numerical differentiation

Given function is

Differentiating w.r.to x

Difference between the approximation and the actual value of f′(0.5) is 0.4330

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

step-by-step explanation:

f(gx)=f(1/x+2)

=(1/x+2)+2

=(1+2x)/2+2

=(1+2x+4)/2

= (2x+5)/2