THEOREM 3.1 Differentiable Implies Continuous If f is differentiable at a, then f is continuous at a Copyright@2011 Pearson Education, Inc. Publishing as Pears on Addison-Wesley Slide 3-21
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If f is not continuous at a, then f is not differentiable at a y=f(r) FIGURE 3. 15 Copyright@2011 Pearson Education, Inc. Publishing as Pears on Addison-Wesley Slide 3-22
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1≠2 implies f(a) does not exist Tangents approach e;asx→a- Tangents approach aSx→a l FIGURE 3. 16 Copyright@2011 Pearson Education, Inc. Publishing as Pears on Addison-Wesley Slide 3-23
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vertical vertical tangent tangent lit lin =vx f(o) does not exist. f(o)does not exist imf(x)=∞ imf"(x)=∞ lim f(r) imf(x)=∞ FIGURE 3. 17 Copyright@2011 Pearson Education, Inc. Publishing as Pears on Addison-Wesley Slide 3-24
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y=g(x) 4-3-2-1 234 FIGURE 3.18 Copyright@2011 Pearson Education, Inc. Publishing as Pears on Addison-Wesley Slide 3-25
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