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Derivative (Derivatives Rules (Inverse (inverse function exists, whenever…

- - - - y is static at that point
    - - y is decreasing at that point
    - - y is increasing at that point
  - - - Accleration
      - Exp: Rate of job growth slows / rate of change in number of jobs which is positive is slowing
- - - - L(x) = f(x)
        L'(x) = f(x)
  - - - P(x) = f(x)
        P'(x) = f'(x)
        P''(x) = f''(x)
    - - L(x) = linear appro. + O(x^2)
        P(x) = quadratic appro. + O(x^3)
      - Big O: Definition
        f(x) = \( O(x^2) \) near x = 0 if f(x) <= \( k.x^2 \) for some constant k
  - - - finding the roots of the objective function, f(x) = 0, for optimization problem (find minima & maxima)
    - - slope of (tangle line) is too small
      - first guess too far from result
- - - - local max or local min
      - corner, just f'(x) = 0
    - - first derivative test
      - second derivative
    - - The point that graph changes its concavity which are either concave up or concave down
  - - - Newton
      - Gradient descent
- - - - f+g, f-g, f*g is continuous everywhere if f,G is continuous
      - f/g: countinous if g not 0 and f,g is continuous