Find the difference quotient of f; that is, find StartFraction f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis Over h EndFraction comma h not equals 0 comma for the following function. f left parenthesis x right parenthesis equals negative 4 x plus 6

-4

Step-by-step explanation:

Given the following function:

f (x) = - 4x + 6

We have to find the difference quotient of f (x); that is,

[f (x + h) - f (x) ]/h

So, we ned to compute f (x + h) as follows:

f (x+h) = - 4 (x+h) + 6 = - 4x - 4h + 6

Replacing into the difference quotient, we get:

[f (x + h) - f (x) ]/h = [-4x - 4h + 6 - (-4x + 6) ]/h

[f (x + h) - f (x) ]/h = [-4x - 4h + 6 + 4x - 6) ]/h

[f (x + h) - f (x) ]/h = [ - 4h) ]/h

[f (x + h) - f (x) ]/h = - 4