April 12th, 2017, 10:33 AM  #1 
Member Joined: Feb 2017 From: henderson Posts: 36 Thanks: 0  Antiderivative graph I really do not know how to start this problem or how to analyze it. Can somebody explain this to me. (PLEASE NO ANSWERS, I NEED TO LEARN THIS) Thank you! 
April 12th, 2017, 11:22 AM  #2 
Senior Member Joined: May 2016 From: USA Posts: 785 Thanks: 312 
Looking at the graph of f(x), what do you think f(x) is?

April 12th, 2017, 12:35 PM  #3 
Math Team Joined: Jul 2011 From: Texas Posts: 2,624 Thanks: 1303  Have you learned what the sign of the derivative tells you about the behavior of a function? What does the sign of the 2nd derivative tell you?

April 12th, 2017, 02:10 PM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,649 Thanks: 680 
Do you see that this graph is a straight line? Do you know that any (nonvertical) line can be written as y= mx+ b? Here, you can see that y(0)= 1 and y(1)= 0. So y(0)= m(0)+ b= b= 1. And y(1)= m(1)+ b= m+ 1= 0. Solve for m. Once you know m and b, F'(x)= mx+ b so F(x) is the integral of that plus a constant. The information that F(0)= 0 allows you to find that constant. 

Tags 
antiderivative, graph 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Antiderivative HELP  fivestar  Calculus  3  September 18th, 2016 07:14 PM 
Antiderivative Help  Shamieh  Calculus  3  November 13th, 2013 01:32 PM 
What is the antiderivative of 4x / (x^2 + 4)?  rajend3  Calculus  2  July 18th, 2009 08:10 AM 
antiderivative of (z^2) ln z  rajend3  Calculus  2  July 18th, 2009 05:03 AM 
Can someone help me with this antiderivative please?  mmmboh  Calculus  3  September 19th, 2008 01:55 PM 