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Differentiation Rules - Products~

  1. Oct 18, 2009 #1
    1. Suppose the curve f(x)=(x^4)+a(x^3)+b(x^2)+cx+d has tangent line when x=0 with equation y=2x+1, and a tangent line when x=1 with equation y=2-3x. Find a,b,c,d



    2. d/dx f(x)g(x)=g*f`+f*g`



    3. f`(x)=4x^3+3ax^2+2bx+c

    x=0 y=2x+1 y=1 (0,1) is a point on f(x)
    x=1 y=2x-3 y=-1 (1,-1) is a point on f(x)

    This question really has me stumped... I just need a hint to get the ball rolling...
     
    Last edited: Oct 18, 2009
  2. jcsd
  3. Oct 18, 2009 #2

    HallsofIvy

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    Okay, so f(0)= d= 1 and f'(0)= c= the slope of y= 2x+1.

    so f(1)= ... and f'(1)= ...

     
  4. Oct 19, 2009 #3
    Ok, then f(1)=a+b+4=-1 and f'(1)=3a+2b+6=-3

    so, a+b+5=0 and 3a+2b+9=0

    then I isolate b in the first equation and sub it into the second to get:
    3a+2(-a-5)+9=0
    a=1

    Then use a to find the value of b

    So my values are: a=1, b=-6, c=2, d=1
     
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