Answered: Is 90 and 92 True or False

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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Is 90 and 92 True or False

Expert Solution

Step 1

90)

Given that f(x)=1/x is concave downward for x<0 and concave upward for x>0 and thus it has a point of inflection at x=0.

We need to check whether the given statement is True or False.

Solution:

To find the inflection point we need to find the second derivative of the function and check where the second derivative of the function is zero.

$f (x) = {x^{-}}^{1} f' (x) = - 1 x^{- 2} f'' (x) - 1 (- 2) x^{- 3} f'' (x) = \frac{2}{x^{3}}$

given that the function as inflection at x=0 but at x=0 the second derivative of the function is not defined and no inflection exists for this function.

Hence the given statement is False.

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