Question

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

Answer 1

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;