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Phytoplankton Growth Researchers have described the maximum growth rate of phytoplankton as a function of the cell diameter x by the equation g(x) = ax² + bx + c' where a, b, and c are positive constants and x > 0. Source: The American Naturalist. For simplicity, let a = b = c = 1. a. The researchers state that when x is small, g'(x) > 0, but when x is large, g'(x) < 0. Find any intervals for which g'(x) > 0, and any for which g' (x) < 0. b. Calculate g"(x).

Phytoplankton Growth Researchers have described the maximum growth rate of phytoplankton as a function of the cell diameter x by the equation g(x) = ax² + bx + c' where a, b, and c are positive constants and x > 0. Source: The American Naturalist. For simplicity, let a = b = c = 1. a. The researchers state that when x is small, g'(x) > 0, but when x is large, g'(x) < 0. Find any intervals for which g'(x) > 0, and any for which g' (x) < 0. b. Calculate g"(x).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Phytoplankton Growth Researchers have described the maximum growth rate of phytoplankton as a function of the cell diameter x by the equation g(x) = ax² + bx + c' where a, b, and c are positive constants and x > 0. Source: The American Naturalist. For simplicity, let a = b = c = 1. a. The researchers state that when x is small, g'(x) > 0, but when x is large, g'(x) < 0. Find any intervals for which g'(x) > 0, and any for which g' (x) < 0. b. Calculate g"(x).
Transcribed Image Text:Phytoplankton Growth Researchers have described the maximum growth rate of phytoplankton as a function of the cell diameter x by the equation g(x) = ax² + bx + c' where a, b, and c are positive constants and x > 0. Source: The American Naturalist. For simplicity, let a = b = c = 1. a. The researchers state that when x is small, g'(x) > 0, but when x is large, g'(x) < 0. Find any intervals for which g'(x) > 0, and any for which g' (x) < 0. b. Calculate g"(x).
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