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 }(f(x+h)-f(x))/(h).`

Step-by-step 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.

`(f(x+h)-f(x))/(h)=(-4h)/(h)`

Cancel out the common multiple h.

`(f(x+h)-f(x))/(h)=-4`

Final answer:

`(f(x+h)-f(x))/(h)=-4`