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Creating a function

  1. Oct 28, 2013 #1
    f: ℝ→ℝ y = 3x²/4+bx+c
    Let P(-1|9) be a point on the function, with a tangent-slope of -6
    Find b and c

    No matter how I calculate, I get b = [itex]\frac{-9}{2}[/itex] and c = [itex]\frac{15}{4}[/itex]
    The solution textbook I have tells me that c is [itex]\frac{-15}{4}[/itex]

    Am I doing something wrong or did they make a typo in the solution textbook? Oo
     
  2. jcsd
  3. Oct 28, 2013 #2

    Mark44

    Staff: Mentor

    Homework-type problems must be posted in the Homework & Coursework section, not in the technical math section. I am moving this post to the Calculus & Beyond section under Homework & Coursework.
     
  4. Oct 28, 2013 #3

    Mark44

    Staff: Mentor

    It would be helpful if you showed us what you did.

    BTW, we write points with a comma separating the coordinates, not a vertical bar. In other words, like this: P(-1, 9).
     
  5. Oct 29, 2013 #4
    Okay, sorry :)

    So what I did was, I got the first derivative y' = 3/2x+b

    Then I set f(-1) = 9 and f'(-1) = -6

    So -6 = 3/2*(-1)+b --> b = -9/2

    9 = 3/4*(-1)² + (-1)*b + c

    9 = 3/4 - b + c

    9 = 3/4 - (-9/2) + c

    9 = 3/4 + 18/4 + c

    9-21/4 = c

    c = 15/4

    --> f: y = 3/4x^2 - 9/2x + 15/4
     
  6. Oct 29, 2013 #5

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You are completely correct and there's a typo in the solution.
     
  7. Oct 29, 2013 #6
    Thank you :)
     
  8. Oct 29, 2013 #7

    Mark44

    Staff: Mentor

    It's easy enough to check. The values you got show that the function is f(x) = (3/4)x2 - (9/2)x + 15/4. You can verify that f(-1) = 9 and that f'(-1) = -6.

    Since your answer differs from the book answer, make sure that you are working the right problem and that you haven't overlooked or added a minus sign somewhere.
     
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