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P.160 P.161 2.2 THE DERIVATIVE 1

2.2 THE DERIVATIVEspaces.isu.edu.tw/upload/19225/0/news/postfile_309.pdf · Find the derivative of f(x) = 3x3 — I at an unspecified value of x. Then, evaluate the derivative at

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Page 1: 2.2 THE DERIVATIVEspaces.isu.edu.tw/upload/19225/0/news/postfile_309.pdf · Find the derivative of f(x) = 3x3 — I at an unspecified value of x. Then, evaluate the derivative at

P.160

P.161

2.2 THE DERIVATIVE

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Page 2: 2.2 THE DERIVATIVEspaces.isu.edu.tw/upload/19225/0/news/postfile_309.pdf · Find the derivative of f(x) = 3x3 — I at an unspecified value of x. Then, evaluate the derivative at

P.162

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Page 3: 2.2 THE DERIVATIVEspaces.isu.edu.tw/upload/19225/0/news/postfile_309.pdf · Find the derivative of f(x) = 3x3 — I at an unspecified value of x. Then, evaluate the derivative at

The value of a derivative at a point is the slope of the tangent line at

that point.

P.163

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Page 4: 2.2 THE DERIVATIVEspaces.isu.edu.tw/upload/19225/0/news/postfile_309.pdf · Find the derivative of f(x) = 3x3 — I at an unspecified value of x. Then, evaluate the derivative at

P.164

Alternative Derivative NotationsP.165

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Page 5: 2.2 THE DERIVATIVEspaces.isu.edu.tw/upload/19225/0/news/postfile_309.pdf · Find the derivative of f(x) = 3x3 — I at an unspecified value of x. Then, evaluate the derivative at

If a function is not continuous at a point then it cannot have a derivative

at that point.

Functions are not differentiable at any point where their graph has a

“sharp” corner

P.166

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