Linear Approximation

• A tangent line to $y=f(x)$ at $x=a$ is
• $y=f(a)+f^{\prime }(a)(x-a)$
• Derivation:

• You can use this to approximate a difficult function at an x value close to an easy number (eg. $(0.97{)}^{\frac{1}{3}}$)
  • Simply set a to the nice number
• Of course, this is extremely bald so use Taylor Series