3+4x 20 7x-2 10 (1,5) Slope of tangent line at(1, 5) -10 Is n 7. FIGURE 3. 6 Copyright@2011 Pearson Education, Inc. Publishing as Pears on Addison-Wesley Slide 3-11
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tan- instantaneous rate of change derivative at b near o m.= instantaneous rate of change derivative at c man instantaneous rate of change m.<0 derivative at a >0 FIGURE 3.7 Copyright@2011 Pearson Education, Inc. Publishing as Pears on Addison-Wesley Slide 3-12
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DEFINITION The Derivative The derivative of f is the function f'(r)=lim f(x+ h)-f(r →0 h provided the limit exists. If f'(r)exists, we say f is differentiable at x. If f is differen tiable at every point of an open interval 1, we say that f is differentiable on 1 Copyright@2011 Pearson Education, Inc. Publishing as Pears on Addison-Wesley Slide 3-13
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150 f(3)=0 f'(2)=32 ∫(4)=-32 100 f(1)=64 16x-+96x f(5)=-64 f(x)=-32x+96 50 f"(0=96 f(6)=-96 FIGURE 3. 8 Copyright@2011 Pearson Education, Inc. Publishing as Pears on Addison-Wesley Slide 3-14
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mon=f(r) sec f(x+△x) △y=f(x+△x)-f(x) f(r) x+△x △ f(x)= lim dy FIGURE 3. 9 Ax→0 △xdx Copyright@2011 Pearson Education, Inc. Publishing as Pears on Addison-Wesley Slide 3-15
Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3 - 15