Explanation Given information: The function is y = x 3 − 5 x 2 + 2 x + 8 . Concept used: A function is concave up and increasing where the first derivative of the function is greater than 0. A function is concave down and decreasing where the first derivative of the function is less than 0. At the point of inflection, a function changes its position from concave up to concave down. Calculation: Consider the function. y = x 3 − 5 x 2 + 2 x + 8 The function is a polynomial function. Now, to check the concavity, point of inflection of the function, let us find the derivative as shown: d y d x = 3 x 2 − 10 x + 2 Now, the first derivative is increasing for d y d x > 0 3 x 2 − 10 x + 2 > 0 x > 0.21370 or x < 3.11963 Therefore, the function is increasing and concave up for the interval ( − ∞ , 0.21370 ) ∪ ( 3

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Student's Solution and Survival Manual for Calculus

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The graph for the given function.

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