Question

Compute the difference quotient StartFraction f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis Over h EndFraction

f(x+h)−f(x)
h for the function f left parenthesis x right parenthesis equals negative 4 x squared minus 3 x minus 4.f(x)=−4x2−3x−4. Simplify your answer as much as possible.
StartFraction f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis Over h EndFraction
f(x+h)−f(x)
hequals=nothing

Answer 1

`(f(x+h) - f(x))/(h)=-8x-4h-3`

Explanation:

`f(x)=-4x^2-3x-4`

`f(x+h)=-4(x+h)^2-3(x+h)-4`

`f(x+h)=-4(x^2+2xh+h^2)-3(x+h)−4`

`f(x+h)=-4x^2-8xh-4h^2-3x-3h-4`

`f(x+h) - f(x)=-4x^2-8xh-4h^2-3x-3h-4-(-4x2-3x-4)`

`f(x+h) - f(x)=-4x^2-8xh-4h^2-3x-3h-4+4x2+3x+4`

`f(x+h) - f(x)=-8xh-4h^2-3h`

`f(x+h) - f(x)=h(-8x-4h-3)`

`(f(x+h) - f(x))/(h)=(h(-8x-4h-3))/(h)`

`(f(x+h) - f(x))/(h)=-8x-4h-3`