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[DOC File]Section 1 - Radford
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Inflection points are points where the concavity of the graph of a function f changes. Note: If is a point of inflection of the graph of f , then either or is undefined. Second Derivative Test (Test For Relative Maximum and Relative Minimum Points) Let f be a function where x = c is a critical point where . 1. If , then is a relative minimum. 2.
second derivative to original function

[DOC File]Chapter 2, sections 2
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3.2 –Extrema and the 1st Derivative Test. know what extrema are (both relative and absolute) be able to find them using the first derivative test. 3.3 –Concavity and the 2nd Derivative Test. understand what the second derivative tells us about the original function . know what “concavity” is and what “inflection points” are & how to ...
function to derivative graph

[DOC File]New Chapter 3
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6.2 The Second Derivative. Since the derivate of a function is a function itself it is possible to take its derivative. The derivative of the first derivative is called the second derivative and it is typically denote using a double prime, . The second derivative of a function is a function …
second derivative of a function

[DOC File]Derivatives - UH
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Now let’s begin seeing the derivative as a function related to our original function that calculates instantaneous rates of change for the original function. It works like this: The original function takes x and computes the second coordinate for the graph point at x. The derivative takes x and computes the instantaneous rate of change of the ...
functions and their derivatives graphs

[DOCX File]NJCTL
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Each graph provided is the graph of the derivative function, f’(x). The domain for each original function f(x) is the set of all real numbers and is continuous everywhere. Use the provided information to create a sketch of each original function.
finding second derivative from graph

[DOC File]GRAPHING OF FUNCTIONS USING FIRST AND SECOND …
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3. If the second derivative f'' is positive (+) , then the function f is concave up . 4. If the second derivative f'' is negative (-) , then the function f is concave down . 5. The point x=a determines a relative maximum for function f if f is continuous at x=a , and the first derivative f' …
first and second derivative graphs

Activity overview:
Find the first derivative of the function y = 2x3 – 3x2 – 12x. Set this function equal to zero and solve. a. What are your solutions? b. What is the name given to these solutions? 3. Find the second derivative of the original function (or the derivative of the first derivative). Evaluate each of the critical numbers in the second derivative. a.
first derivative second derivative graph

[DOC File]Relationship between the Derivative and the Integral and ...
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Relationship between the Derivative and the Integral and the Graphs. Mini-Project -- 30 points. Due by 6:41 a.m. on Monday, 3/13/17. This is the second of 4 problems designed to help you solidify your understanding of major calculus topics.
derivative graph to original function

[DOC File]Derivatives and Graphing Internet Activity:
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It is an Applet: On the definition of the derivative. A new window will open. Move the slide bar at the bottom. This illustrates the slope of the tangent line at different x-values on a graph. Close the window when you are done. The next three red boxes on the right are matching first and second derivative graphs with the original function.
second derivative to original function

[DOC File]Assignments Differentiation
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For each derivative graphed below draw a possible graph of the original function ƒ. a. b. c. 6. Sketch a graph of the derivative of each of the following functions. a. ... A continuous function f has first derivative and second derivative . a. Determine the intervals on which f is increasing and decreasing and find and classify the relative ...
function to derivative graph

Second derivative graph to original function