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# 4.3b - Let ′ f x)= 4 x 3-12 x 2 a Identify where the...

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Calculus Section 4.3 Page13 4.3b More Connecting f and f with the Graph of f Look at Graph Summary Example 1 Using the First and Second Derivative Draw a possible graph, given each set of conditions a) f 2 ( ) = 4, f 2 ( ) < 0, ′′ f 2 ( ) < 0 b) f 2 ( ) = 4, f 2 ( ) > 0, ′′ f 2 ( ) > 0 c) f 2 ( ) = 4, f 2 ( ) = 0, f 2 ( ) < 0 d) f 2 ( ) = 4, f 2 ( ) = 0, f x ( ) < 0 for x < 2, f x ( ) > 0 for x > 2 d) f is an even function, continuous on - 3, 3 [ ] x 0 1 2 3 x 0 < x < 1 1 < x < 2 2 < x < 3 f 2 0 –1 0 f + f undef 0 undef 0 f + f undef 0 undef 0 f + Example 2 A function f is continuous on its domain - 2, 4 [ ] . f - 2 ( ) = 5, f 4 ( ) = 1 , and f and f have the following properties. x - 2 < x < 0 x = 0 0 < x < 2 x = 2 2 < x < 4 f + does not exist 0 f + does not exist + 0

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Calculus Section 4.3 Page 14 a) Find where all absolute extrema of f occur. b) Find where the points of inflection of f occur. c) Sketch a possible graph of f . Example 3 Finding the Points of Inflection Let
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Unformatted text preview: Let ′ f x ( )= 4 x 3-12 x 2 a) Identify where the extrema of f occur. b) Find the intervals on which f is increasing the intervals on which f is decreasing. c) Find where the graph of f is concave up and where it is concave down. d) Sketch a possible graph for f . (Just show shape – not location of points) Calculus Section 4.3 Page15 Example 4 Using the Graph of f Use the graph of the function f to estimate where a) ′ f and b) ′ ′ f are 0, positive, and negative. Example 5 Using the Graph of ′ f Use the graph of ′ f to draw the corresponding thumbnail. Then estimate the intervals on which the function f is a) increasing or b) decreasing. c) Estimate where f has local extreme values Assignment III-3b Pages 203 – 205 #1 – 6 all*, 33, 34, 37, 39, 41, 43, 45, 47, 48, Graphing Session II Sheet –2 2 y = f x ( ) –2 2 y = f x ( ) y = ′ f x ( ) y = ′ f x ( )...
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4.3b - Let ′ f x)= 4 x 3-12 x 2 a Identify where the...

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