Question

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

Answer 1

-4

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