If $f$ is differentiable at $x=a$, then the approximating function $L(x)=f(a)+f^{\prime}(a)(x-a)$ is the **linearization** of $f$ at $a$. The approximation $f(x) \approx L(x)$ of $ƒ$ by $L$ is the *standard linear approximation* of $ƒ$ at $a$. The point $x = a$ is the center of the approximation. $f(a+\Delta x)\approx f(a)+\Delta L$ The *linear approximation error* is the difference between the the approximation and the actual value. $\epsilon=\Delta y+\Delta L$ ![[Screen Shot 2022-04-15 at 10.23.20 AM.png]] This is a loosening of the idea a differential approximation,