In Figure 3, is graph (A) or graph (B) the

angepepagiortzb

angepepagiortzb

Answered question

2021-12-04

In Figure 3, is graph (A) or graph (B) the graph of an antiderivative of
y=f(x)?

Answer & Explanation

Louis Smith

Louis Smith

Beginner2021-12-05Added 14 answers

Step1
Option Ais the correct graph.
Use the fundamental theorem for calculus.
Iff(x)=g(x)
Then, ddxf(x)=g(x)
Therefore, f(x) is the graph for the derivative for either A or B.
Step2
Check if the f(x) is possible derivative for A using the graphical approach.
The function of the graph Ais of polynomial of degree greeter than 2 as the graph of the derivative ie. f(x) is curve and not straight line.
The function for graph A=6xsinx+6cosx8
Derivative for graph A=6sinx+6xcosx6sinx
=6xcosx


Step3
Plot the graphs for A and the derivative of A.
Step4
The red graph matches with the graph for y=f(x).
Thus, y=f(x) is the derivative for graph A.
Hence, graph A is the antiderivative for y=f(x) and the option Ais the correct choice.

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