Question

Given f(x)=x^2+4x+5, what is f(2+h)-f(2)/h equal to?A. h^2 + 8hB. 2x + h + 4C. 8 + hD. h + 4

Answer 1

C. 8 + h

Explanation:

We have the following expression:

`f\mleft(x\mright)=x^2+4x+5`

We evaluate each case and obtain the following:

`\begin{gathered} f(h+2)=\left(2+h\right)^2+4\left(2+h\right)+5 \\ \\ f(2+h)=4+4h+h^2+8+4h+5 \\ \\ f(2+h)=h^2+4h+4h+4+8+5 \\ \\ f(2+h)=h^2+8h+17 \\ \\ \\ f(2)=\left(2\right)^2+4\left(2\right)+5 \\ \\ f(2)=4+8+5 \\ \\ f(2)=17 \end{gathered}`

We substitute each function evaluated to determine the final result, just like this:

`\begin{gathered} (f(2+h)-f(2))/(h)=(h^2+8h+17-17)/(h) \\ \\ (f(2+h)-f(2))/(h)=(h^2+8h)/(h) \\ \\ (f(2+h)-f(2))/(h)=h+8=8+h \end{gathered}`

Therefore, the correct answer is C. 8 + h