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OLEGan [10]
3 years ago
9

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

enthesis 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
Mathematics
1 answer:
kenny6666 [7]3 years ago
7 0

Answer:

\dfrac{f(x+h) - f(x)}{h}=-8x-4h-3

Step-by-step 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)

\dfrac{f(x+h) - f(x)}{h}=\dfrac{h(-8x-4h-3)}{h}

\dfrac{f(x+h) - f(x)}{h}=-8x-4h-3

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