Question

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!

Answer 1

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)
v(1+2)+c=(1+c)+6
3v+c=v+c+6
-c -c
3v=v+6
-v -v
2v=6
v=3

then put or newly obtained v value into f(1)=10
f(t)=vt+c
3(1)+c=10
3+c=10
c=7

3t+7

So frustrating, I'm getting for calculus this fall and I'm struggling from the start!

Answer 2

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
f(3)= 16
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 \[(y -ya) /( yb -ya) = (x - xa) / (xb - xa)\]
Byee:)

Answer 3

Thank you that is actually a lot easier!