Explanation Given information: The function is, f ( x ) = x 3 e − 1 / x (1) With x = − 1 . Formula used: The formula to calculate the differential of a function f ( u ⋅ v ) by Product Rule is, f ( u ⋅ v ) = u d d x ( v ) − v d d x ( u ) [ u , v are functions of same variable ] . Calculation: Differentiate both sides of the equation (1) with respect to x by product rule. f ′ ( x ) = d d x ( x 3 e − 1 / x ) = x 3 d d x ( e − 1 / x ) + e − 1 / x d d x ( x 3 ) = x 3 ( e − 1 / x ) d d x ( − x − 1 ) + e − 1 / x ( 3 x 2 ) [ ∵ d d x ( e f ( x ) ) = e f ( x ) ( f ′ ( x ) ) ] = − x 3 ( e − 1 / x ) ( − 1 x − 1 − 1 ) + e − 1 / x ( 3 x 2 ) [ ∵ d d x ( x n ) = n x n − 1 ] Further simplify the above equation

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

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ISBN: 9780357465400

Author: Tan

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Chapter 5.4, Problem 1TE

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To find: The rate of change of function f(x)=x3e−1/x at the given value of x by numerical derivative operation.

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Chapter 5.4, Problem 92E

Chapter 5.4, Problem 2TE

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Let g be the following function that gives the values of y in terms of the values of x.\\\\ g(x) = 12 – 5*. (a) Use proper function notation to write the formula that gives the average rate of change of y (w.r.t. x) as x goes from x = -1 to x = 1. (b) Calculate (an intermediate step) and simplify the output g(1); (c) Calculate (an intermediate step) and simplify the output g(-1); (d) Compute the value of average rate of change (described in part a) . Previous Page Next Page Page 15 of 17

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Chapter 5 Solutions

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

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The rate of change of function f ( x ) = x 3 e − 1 / x at the given value of x by numerical derivative operation.

Solution Summary: The author calculates the differential of a function f(ucdot v) by product rule.

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To find: The rate of change of function f(x)=x3e−1/x at the given value of x by numerical derivative operation.

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Chapter 5 Solutions