Explanation Given information: The function f ( x ) = x ln x and x 0 = 1 Concept and Formula Used: Instantaneous Rate of change - The instantaneous rate of change of a function f ( x ) at x = x 0 is the value of the derivatie of f ( x ) at x = x 0 and is given by: Instantaneous rate of change = f ' ( x 0 ) = [ d d x f ( x ) ] x = x 0 and formula d d x ( u . v ) = v d d x u + u d d x v , d d x ( x n ) = n x n − 1 , d d x ( ln x ) = 1 x , ln ( a ) b = b ln a . Calculation: It is given that f ( x ) = x ln x Using the property ln ( a ) b = b ln a , f ( x ) = x ln x can be written as f ( x ) = x ln ( x ) 1 2 = 1 2 x ( ln x ) First find the derivative of f ( x ) = 1 2 x ( ln x ) d d x f ( x ) = [ 1 2 x ( ln x ) ] using product rule of derivative d d x ( u

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ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 3.4, Problem 10PS

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To Calculate: The instantaneous rate of change of f(x)=xlnx with respect to xat x0=1

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Chapter 3.4, Problem 9PS

Chapter 3.4, Problem 11PS

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8:38 *** TEMU TEMU -3 -2 7 B 2 1 & 5G. 61% 1 2 -1 Based on the graph above, determine the amplitude, period, midline, and equation of the function. Use f(x) as the output. Amplitude: 2 Period: 2 Midline: 2 ☑ syntax error: this is not an equation. Function: f(x) = −2 cos(πx + 2.5π) +2× Question Help: Worked Example 1 ☑ Message instructor Submit Question ||| <

Chapter 3 Solutions

Calculus

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The instantaneous rate of change of f ( x ) = x ln x with respect to x at x 0 = 1

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Chapter 3 Solutions