I have a question from the book "Calculus" by Gilbert Strang. It's available for download here.
Anyway on p7 is the question:
Find the linear function with f(t+2)=f(t)+6 and f(1)=10. The answer is 3t+7. I cannot even begin to figure out a way to find this out. please help, thanks!
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Never mind, I figured it out... had to go through an old math book. If anyone is wondering:
First you need to solve for the slope by substituting the known value of f(1):
f(t)=vt+C (the goofy notation for slope-intercept used in this section of the book)
then put or newly obtained v value into f(1)=10
So frustrating, I'm getting for calculus this fall and I'm struggling from the start!
Hi!! I think you can solve the problem also by this way.
You Know that f(1) = 10
So f(1 +2) = f(1) +6 I have only replaced t=1
Now you have two point A(1;10) and B(3;16) , and you can use this formula to find the equation of the linear function \[(y -ya) /( yb -ya) = (x - xa) / (xb - xa)\]