Calc03_2&amp;3_3

# Calc03_2&amp;3_3 - 3.2 Differentiability No Yes Yes Yes...

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3.2 Differentiability

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Yes Yes Yes No No
All Reals 0, ÷ 3, ÷ 3.2 5

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To be differentiable, a function must be continuous and smooth . Derivatives will fail to exist at: corner cusp vertical tangent discontinuity ( 29 f x x = ( 29 2 3 f x x = ( 29 3 f x x = ( 29 1, 0 1, 0 x f x x - < ì = í ³ î
Most of the functions we study in calculus will be differentiable.

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Derivatives on the TI-89: You must be able to calculate derivatives with the calculator and without. Today you will be using your calculator, but be sure to do them by hand when called for. Remember that half the test is no calculator .
3 y x = Example: Find at x = 2 . dy dx d ( x ^ 3, x ) ENTER returns 2 3 x This is the derivative symbol, which is . 8 2nd It is not a lower case letter “d”. Use the up arrow key to highlight and press . 2 3 x ENTER 3 ^ 2 2 x x = ENTER returns 12 or use: ( 29 ^ 3, 2 d x x x = ENTER

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The calculator may return an incorrect value if you evaluate a derivative at a point where the function is not differentiable. Examples:
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Calc03_2&amp;3_3 - 3.2 Differentiability No Yes Yes Yes...

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