Differential Calc

posted by .

If:

0 = f(1) = a+b+c+d
2 = f(-2) = -8a+4b-2c+d
0 = f'(1) = 3a+2b+c
0 = f'(-2) = 12a-4b+c

"since we now have four equations and four unknowns, we can determine unique solution. Solving for "a" and "b", a=, b="

Please show the steps, I am so confused and no one knows how to do it.

Thank you so much in advance!

  • Differential Calc -

    apparently f(x) = ax^3 + bx^2 + cx + d
    so f'(x) = 3ax^2 + 2bx + c

    and you were given f(1), f(-2) and f'(1), f'(-2)

    take the last two equations, equate c:

    3a+2b = 12a-4b
    6b = 9a
    2b = 3a

    take the first two equations, equate d:
    a+b+c = -8a+4b-2c
    so,
    2a+2b+2c = -16a+8b-4c
    but 2b = 3a, so
    2a+3a+c = -16a + 12a - 4c
    9a = -5c

    start substituting those values back in, and you get

    a,b,c,d = 4/27, 2/9, -8/9, 14/27

    y = 1/27 (4x^3 + 6x^2 - 24x + 14)
    = 2/27(x-1)^2 (2x+7)
    f(1) = 0 and f(-2) = 2

    y' = 4/9 (x^2 + x - 2) = 4/9 (x+2)(x-1)
    it's easy to see that f'(1) = f'(-2) = 0

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    Can someone please help me with an algebra problem?
  2. math

    3x+y=-4 x=3-3y y=2x x+2y=-4 You have written four equations in two unknowns. There is no x,y combination that satisfies all of them. What is your question?
  3. Predicting products for electrolysis

    when you have your 4 different equations to form 4 different possible equations, what two equations do you use for water, O2(aq) + 4H+ + 4e- ----> 2H20 (+1.23) 02 (g) + 2H2O (l) + 4e- ----> 4OH- (+0.40) 2H20 (l) + 2e- ---> …
  4. math age problem

    four years agoslyvia was two thirds as old as alex was then. four years from now, she will be four fifths as old as alex will be. how old are sylvia and alex now?
  5. calculus

    is y = x^3 a solution to the differential equation xy'-3y=0?
  6. math-calculus

    solving equations with two absolute value brackets |x+4| = |x-2| so i want to know how to do this?
  7. Algebra

    Suppose a linear system of equations has 2012 equations and 2013 unknowns. Answer the following questions:  Can the system be inconsistent?
  8. Vectors

    How to solve a system of equations if there are FOUR equations with THREE unknowns?
  9. Differentail Equations

    I cant figure out how to do this type of problem! Consider the first order differential equation y′+(x/(x^2−4))y=(e^x)/(x−9) For each of the initial conditions below, determine the largest interval a<x<b on …
  10. Differential equations,Calculus

    So I have the following differential equation. The general solution I have is: t=k(-1/r)+c I now need to find the particular solution when t=0 and the radius (r) = 1cm. So k is a constant which is approx 3.9 (5/4pi) So for the particular …

More Similar Questions