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Suppose that y = f(r) is a continuous function defined on the interval from z = 0 to x = E. Below is a graph of f'(x), the derivative of f(x), which is defined at all points of [0, E] except at x = C. MJ B 0 D E (a) Where is f(x) increasing? Where is f(x) decreasing? Where does f(x) have local extreme values (for 0

Suppose that y = f(r) is a continuous function defined on the interval from z = 0 to x = E. Below is a graph of f'(x), the derivative of f(x), which is defined at all points of [0, E] except at x = C. MJ B 0 D E (a) Where is f(x) increasing? Where is f(x) decreasing? Where does f(x) have local extreme values (for 0

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 12CR: Determine whether each of the following statements is true or false and explain why. The derivative...
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Question 1 and 2 please. Thanks !
1. Suppose that y = f(x) is a continuous function defined on the interval from x = 0 to x = E. Below is a graph of f'(x), the derivative of f(x), which is defined at all points of [0, E] except at x = C. NA B 0 A E (a) Where is f(x) increasing? Where is f(x) decreasing? Where does f(x) have local extreme values (for 0< x < E)? (b) Where is f(x) concave up? Where is f(x) concave down? Where does f(x) have inflection points? (c) Draw a possible graph of f(x) which uses all of the information given and deduced about f(x).
Transcribed Image Text:1. Suppose that y = f(x) is a continuous function defined on the interval from x = 0 to x = E. Below is a graph of f'(x), the derivative of f(x), which is defined at all points of [0, E] except at x = C. NA B 0 A E (a) Where is f(x) increasing? Where is f(x) decreasing? Where does f(x) have local extreme values (for 0< x < E)? (b) Where is f(x) concave up? Where is f(x) concave down? Where does f(x) have inflection points? (c) Draw a possible graph of f(x) which uses all of the information given and deduced about f(x).
2. Let f(x) = The first two derivatives of f are f'(x) = -2x (x²+3)² 6(x²-1) (x²- 2+3)³* x²+3 Complete the following table. (Some of the answers may be "none".) After you complete the table, use the information to sketch the graph of f(x). (You may take a picture of this table and turn it in as part of your submission for question #3.) Interval(s) where f is increasing: Interval(s) where f is decreasing: Interval(s) where f is concave up: Interval(s) where f is concave down: r value(s) where f has a local max: x value(s) where f has a local min: r value(s) where f has an inflection point: Equation(s) of horizontal asymptote(s) of f: Equation(s) of vertical asymptote(s) of f: and f"(x) =
Transcribed Image Text:2. Let f(x) = The first two derivatives of f are f'(x) = -2x (x²+3)² 6(x²-1) (x²- 2+3)³* x²+3 Complete the following table. (Some of the answers may be "none".) After you complete the table, use the information to sketch the graph of f(x). (You may take a picture of this table and turn it in as part of your submission for question #3.) Interval(s) where f is increasing: Interval(s) where f is decreasing: Interval(s) where f is concave up: Interval(s) where f is concave down: r value(s) where f has a local max: x value(s) where f has a local min: r value(s) where f has an inflection point: Equation(s) of horizontal asymptote(s) of f: Equation(s) of vertical asymptote(s) of f: and f"(x) =
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