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4x2 + 4x - 1, evaluate and fully simplify each of the - For the function f(0) following f(s + h) f(x + h) - f(5) h 10

4x2 + 4x - 1, evaluate and fully simplify each of the - For the function f(0) following-example-1
User Michalduda
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Given the function f(x);


f(x)=-4x^2+4x-1

Evaluating the function f(x+h);


\begin{gathered} f(x+h)=-4(x+h)^2+4(x+h)-1 \\ f(x+h)=-4(x^2+2xh+h^2)^{}+4(x+h)-1 \\ f(x+h)=-4x^2-4h^2-8xh^{}+4x+4h-1 \end{gathered}

So;


f(x+h)=-4x^2-4h^2-8xh^{}+4x+4h-1

Evaluating the second function;


\begin{gathered} (f(x+h)-f(x))/(h)=\frac{-4x^2-4h^2-8xh^{}+4x+4h-1-(-4x^2+4x-1)}{h} \\ (f(x+h)-f(x))/(h)=\frac{-4x^2-4h^2-8xh^{}+4x+4h-1+4x^2-4x+1}{h} \\ (f(x+h)-f(x))/(h)=\frac{-4x^2+4x^2-4h^2-8xh^{}+4x-4x+4h-1+1}{h} \\ (f(x+h)-f(x))/(h)=\frac{-4h^2-8xh^{}+4h}{h} \end{gathered}

simplifying further;


\begin{gathered} (f(x+h)-f(x))/(h)=\frac{-4h^2-8xh^{}+4h}{h}=-4h-8x+4 \\ (f(x+h)-f(x))/(h)=-4h-8x+4 \end{gathered}

Therefore, we have;


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User NelDav
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