Question

Find and simplify the difference quotient for the following function

Answer 1

`f(x)=-4x^2+7x+4`
`\begin{gathered} f(x+h)=-4(x+h)^2+7(x+h)+4 \\ f(x+h)=-4(x^2+2xh+h^2)+7x+7h+4 \\ f(x+h)=-4x^2-8xh-4h^2+7x+7h+4 \end{gathered}`

Therefore:

`\begin{gathered} (f(x+h)-f(x))/(h)=(-4x^2-8xh-h^2+7x+7h+4-(-4x^2+7x+4))/(h) \\ (f(x+h)-f(x))/(h)=(7h-8xh-h^2)/(h) \\ (f(x+h)-f(x))/(h)=(h(7-8x-h))/(h) \\ (f(x+h)-f(x))/(h)=7-8x-h \end{gathered}`