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anonymous

  • 5 years ago

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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  1. anonymous
    • 5 years ago
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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) 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!

  2. anonymous
    • 5 years ago
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    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:)

  3. anonymous
    • 5 years ago
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    Thank you that is actually a lot easier!

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