Question

If $f\left(x\right)=Ax+B$ and $f\left(0\right)=f\text{'}\left(x\right)=2$ then $f\left(1\right)=$

• A. $4$
• B. $2$
• C. $1$
• D. $-4$

Answer 1

The correct option is A

$4$

Explanation for the correct option.

Find the value of $f\left(1\right)$:

$\begin{array}{rcl}f\left(x\right)& =& Ax+B\\ & \Rightarrow & f\left(0\right)=B\\ \Rightarrow B& =& 2\end{array}$

$$\begin{gathered} f\text{'}\left(x\right)=A \\ \Rightarrow A=2 \end{gathered}$$

So,

$\begin{array}{rcl}f\left(x\right)& =& 2x+2\\ & \Rightarrow & f\left(1\right)=2\left(1\right)+2\\ & =& 4\end{array}$

Hence, option A is correct.