Question

Calculate the difference quotients for f(x) = 4 - Sx using h = 0.1, 0.01, and 0.001. Use the results to approximate the slope of the tangent line to the graph of f(x)at the point (4. - 16). If necessary, round the difference quotients to no less than six decimal places and round your final answer to two decimal places.

Answer 1

Lets remenber the "difference quotient" to a given function f(x):

$\frac{f(x+h)-f(x)}{h}$

Wich give us an aproximation for the slope of a tangent line in a point.

Lets see our expression with the function:

$f(x)=4-5x\text{ , when h=0.1 , h=0.01 and h=0.001}$

We end with the following expressions:

$\frac{(4-5x\text{ + 0.1) - (4-5x)}}{0.1}\text{ , }\frac{(4-5x\text{ + 0.01) - (4-5x)}}{0.01}\text{ , }\frac{(4-5x\text{ + 0.001) - (4-5x)}}{0.001}$