Calc04_3 - 4.3 Using Derivatives for Curve Sketching ( 2, 2...

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4.3 Using Derivatives for Curve Sketching
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- 2,2 ( ) - 3,0 ( ) È 3,¥ ( ) f : all reals f -1 αλλρεαλσ f : all reals f -1 ξ ≠ 0 f : x ≠1 φ -1 ξ ≠1
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y = 0 y = 0 y = 0 ανδ ψ= 300 y = 0 ανδ ψ= 150
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Example γ (ξ29 = ε ξ ξ 2 -3 ( 29 + ε ξ ( 29 = ε ξ ξ 2 + 2ξ -3 ( 29 = ε ξ ξ + 3 ( 29 ξ -1 ( 29 γ (ξ29 = 0 ατξ = -3, 1 γ (ξ29 + | - | + -3 1 Ρελατιωε μ αξ ατ -3,6ε -3 ( 29 , νο αβσολυτε μ αξ Ρελατιωε ανδ αβσολυτε μ ιν ατ 1,-2ε ( 29 Use the first derivative test to find the local and absolute extreme values of: ( 29 2 x g(x) = x - 3 e
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In the past, one of the important uses of derivatives was as an aid in curve sketching. Even though we usually use a calculator or computer to draw complicated graphs, it is still important to understand the relationships between derivatives and graphs.
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y is positive Curve is rising. y is negative Curve is falling. y is zero Possible local maximum or minimum. Second derivative: y ′′ is positive Curve is concave up. y
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Calc04_3 - 4.3 Using Derivatives for Curve Sketching ( 2, 2...

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