Chapter 3.2- Differentiability

# Chapter 3.2- Differentiability - If a function is...

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Differentiability In order for f(x) to be differentiable at x=c F(x) must be continuous at c The limit as x approaches c of f '(c) exists LHD [f(c)] = RHD [f(x)] The Four Types of Non-Differentiability Corner Point Example: the absolute graph y = |x| Cusp Point F(x) = x^(2/3) Vertical tangent F(x) = x^(1/3) Discontinuities Piece-Wise Locally Linear Def: on a close enough scale, the curve will resemble it's tangent line Differentiability implies Continuity

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Unformatted text preview: If a function is differentiable at x=c, then the function is continuous at x=c ◦ Intermediate Value Theorem for Derivatives • Def: if a function is differentiable on [a,b], then the function takes on all ◦ slopes from f'(a) to f'(b) Can help tell that the slope is 0 at a point and therefore establish either ◦ minimums or maximums Symmetric Differentiation (Calculator) • Example 1 MATH. ..8:nDeriv. ..(Function,X,a) ◦ Symmetric Differentiation...
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Chapter 3.2- Differentiability - If a function is...

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