Question

Find the difference quotientf (x+h)-f(x)hwhere h#0, for the function below.f (x)=-4x+5Simplify your answer as much as possible.f(x+h)-f(x)

Answer 1

Given:

$f(x)=-4x+5$

Required:

$\text{We need to find }\frac{f(x+h)-f(x)}{h}.$

Explanation:

$f(x)=-4x+5$

Replace x =x+h in the function f(x).

$f(x+h)=-4(x+h)+5$

$f(x+h)=-4x-4h+5$

Substract the function f(x) from f(x+h).

$f(x+h)-f(x)=-4x-4h+5-(-4x+5)$

Distribute minus sign.

$f(x+h)-f(x)=-4x-4h+5+4x-5$

add the like terms which are like with the same variable with the same power.

$f(x+h)-f(x)=-4x+4x-4h+5-5$

$f(x+h)-f(x)=-4h$

Divide both sides of the equation by h.

$\frac{f(x+h)-f(x)}{h}=\frac{-4h}{h}$

Cancel out the common multiple h.

$\frac{f(x+h)-f(x)}{h}=-4$

Final answer:

$\frac{f(x+h)-f(x)}{h}=-4$