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Applications of the First Derivative Applications of the Second Derivative Curve Sketching

4. Applications of the First Derivative Applications of the Second Derivative Curve Sketching Optimization I Optimization II. Applications of the Derivative. 4.1. Applications of the First Derivative. Increasing and Decreasing Functions.

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CHAPTER 3 SECTION 3.6 CURVE SKETCHING

CHAPTER 3 SECTION 3.6 CURVE SKETCHING. Graph the following functions on your calculator and make a sketch. What do you notice about the graph of a function where there is a factor that appears twice?. 1) y=(x+1)(x-2) 2 2) y= x(x+3) 2 3) y=(x+1)(x-3) 2.

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4.3 Derivatives and the shapes of graphs 4.4 Curve Sketching

4.3 Derivatives and the shapes of graphs 4.4 Curve Sketching. Derivatives and the shapes of graphs. Increasing / Decreasing Test: If f ? (x) > 0 on an interval, then f is increasing on that interval. If f ? (x) < 0 on an interval, then f is decreasing on that interval.

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Applications of the First Derivative Applications of the Second Derivative Curve Sketching

CHAPTER 3 SECTION 3.6 CURVE SKETCHING

4.3 Derivatives and the shapes of graphs 4.4 Curve Sketching