April 12th, 2017, 11:33 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, 12:22 PM  #2 
Senior Member Joined: May 2016 From: USA Posts: 823 Thanks: 335 
Looking at the graph of f(x), what do you think f(x) is?

April 12th, 2017, 01:35 PM  #3 
Math Team Joined: Jul 2011 From: Texas Posts: 2,656 Thanks: 1327  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, 03:10 PM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,822 Thanks: 750 
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. 

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