O (A) p and ronlyO (B) q and s only38. The graph of f', the derivative of f, is shown in the figure above. The function f has a point of inflection at x =O (C) p, r, and tonlyWO (D) q, s, and tonly9Graph of f'

Given information:The graph of the function shown below is of where is the derivative of .To…

Answered: W 9 O(A) and ronl Graph of f' 38. The…

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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Related questions

Question

O (A) p and ronly
O (B) q and s only
38. The graph of f', the derivative of f, is shown in the figure above. The function f has a point of inflection at x =
O (C) p, r, and tonly
W
O (D) q, s, and tonly
9
Graph of f'

Expert Solution

Step 1: Introduction:

Given information:

The graph of the function shown below is of $f apostrophe left parenthesis x right parenthesis$ where $f apostrophe left parenthesis x right parenthesis$ is the derivative of $f left parenthesis x right parenthesis$ .

To find:

The point of inflection of $f left parenthesis x right parenthesis$ .

Concept used:

We say that a point a is an inflection point for the function f if:

i) f is continuous at the point a, and,

ii) f changes concavity at a.

Concavity of a function $f left parenthesis x right parenthesis$ :

A function is said to be concave upward on an interval if, on this interval, all the tangent lines lie below the curve,

i.e., the slope of the tangent lines increases on this interval.

A function is said to be concave downward on an interval if, on this interval, all the tangent lines lie above the

curve, i.e., the slope of the tangent lines decreases on this interval.

Since the given graph is for the derivative of the function $f left parenthesis x right parenthesis$ , i.e., for $f apostrophe left parenthesis x right parenthesis$ and we know that, $f apostrophe left parenthesis x right parenthesis$ is equal to the

slope of the tangent line at x, we can analyze it as:

The function will be said to be concave upward on an interval if $f apostrophe left parenthesis x right parenthesis$ increases on this interval. Similarly, the

function will be said to be concave downward on an interval if $f apostrophe left parenthesis x right parenthesis$ decreases on the given interval.