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Lachlan1996

  • 2 years ago

given that f(x) = ax^3 + bx^2, f(2)=-4 and f'(3)=99 find f(x), f(3) and f'(2)

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  1. Lachlan1996
    • 2 years ago
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    i cant find a way to isolate a or b to solve

  2. tjones89
    • 2 years ago
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    have you found the derivative?

  3. Lachlan1996
    • 2 years ago
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    the derivative is 3ax^2 + 2bx but that doesnt help solve it

  4. mathslover
    • 2 years ago
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    f(x) = ax^3 + bx^2 f(2) = 8a + 4b = -4 f(3) = 27a + 9b = 99

  5. mathslover
    • 2 years ago
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    8a + 4b = -4 27a+9b=99 from equation 1 , we have : a = \(\LARGE\frac{-4-4b}{8}=\frac{-1-b}{2}\) put this value in the second equation.

  6. mathslover
    • 2 years ago
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    Can you now solve for a, b ? @Lachlan1996

  7. Lachlan1996
    • 2 years ago
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    wait wait, hold on youve lost me here.

  8. mathslover
    • 2 years ago
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    lol, take your time. Sorry :)

  9. Lachlan1996
    • 2 years ago
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    uhhh i got 27a + 6b =99 but that is the gradient as in the derivative

  10. Lachlan1996
    • 2 years ago
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    so i dont think you can simultaneously solve it

  11. Lachlan1996
    • 2 years ago
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    because you are simultaneously solving a derivative and a point

  12. EulerGroupie
    • 2 years ago
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    Yes! Now use the f(2)=-4 in the original equation to get your second equation with the two unknowns... a and b

  13. EulerGroupie
    • 2 years ago
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    Two equations with two unknowns should be solvable. Pick your favorite method for solving systems... @mathslover is using substitution.

  14. Lachlan1996
    • 2 years ago
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    but he is solving a f' (x) with a f (x)

  15. EulerGroupie
    • 2 years ago
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    a and b will be the same in the original and the derivative

  16. Lachlan1996
    • 2 years ago
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    ah yes i see

  17. mathslover
    • 2 years ago
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    f(2) = 8a + 4b = -4 f(3) = 27a + 9b = 99 a = (-1-b)/2 put this in f(3) equation. 27(-1-b)/2 + 9b = 99 (-27-27b+18b)=198 -27 -9b = 198 -9b = 198+27 = 225 b = -225/9 b = -25 You can solve for a now.

  18. Lachlan1996
    • 2 years ago
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    in the above equation isnt it meant to be 6a not 9a though?

  19. Lachlan1996
    • 2 years ago
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    wait no i mean 6b not 9b

  20. EulerGroupie
    • 2 years ago
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    Its actually a really cool way to come up with a system... one eq from the original and one from the derivative. Slick, huh?! correct... I got 6b rather than 9b as well

  21. EulerGroupie
    • 2 years ago
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    27a+6b=99 8a+ 4b=-4

  22. Lachlan1996
    • 2 years ago
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    uhh okie doke so a=0.5b-0.5

  23. Lachlan1996
    • 2 years ago
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    however substituting that into 27a + 6b = 99 i got 8.333333 as being b

  24. EulerGroupie
    • 2 years ago
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    I got a=7, b=-15

  25. Lachlan1996
    • 2 years ago
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    oh no made an error forgot to subtract 6b

  26. mathslover
    • 2 years ago
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    OH MY FAULT , sorry :(

  27. Lachlan1996
    • 2 years ago
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    no, no it was a simple mistake, i just wasnt sure if you had made a mistake or were doing something else

  28. Lachlan1996
    • 2 years ago
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    this seems like alot of work just to start off the question, do you think this would be in an exam?

  29. mathslover
    • 2 years ago
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    Depends but I do think, Yep! :)

  30. EulerGroupie
    • 2 years ago
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    For calculus, it doesn't seem out of bounds for a test.

  31. Lachlan1996
    • 2 years ago
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    ahh god, in a year 11 maths exam? i think im buggered then

  32. mathslover
    • 2 years ago
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    Whether it will come or not in exam but I think you must be PREPARED

  33. Lachlan1996
    • 2 years ago
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    mmm yes my exam is in 5 weeks.

  34. EulerGroupie
    • 2 years ago
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    Creating a small system and solving it with substitution is fairly standard in calculus.

  35. mathslover
    • 2 years ago
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    You have much time for it, go through these type of questions and ask your problems here...

  36. Lachlan1996
    • 2 years ago
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    okie doke, thanks very much for the help mate, its much appreciated. thankyou to you both

  37. EulerGroupie
    • 2 years ago
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    You're welcome.

  38. mathslover
    • 2 years ago
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    Welcome! :)

  39. Lachlan1996
    • 2 years ago
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    uhhhh small problem

  40. Lachlan1996
    • 2 years ago
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    we got the answer wrong? its meant to be y=7x^3 -15x^2

  41. mathslover
    • 2 years ago
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    Try to do it again, I think calculation mistake?

  42. EulerGroupie
    • 2 years ago
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    yes... a=7, b= -15

  43. Lachlan1996
    • 2 years ago
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    ah yes, last step of my working didnt put the -ve in the 15

  44. mathslover
    • 2 years ago
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    hmn, Take care of these small mistakes .

  45. EulerGroupie
    • 2 years ago
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    whew! you scared me ;)

  46. Lachlan1996
    • 2 years ago
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    will do, doesnt help when you get frustrated but. maths is not easy for me

  47. sauravshakya
    • 2 years ago
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    I think it is f'(3)=99 not f(3)=99

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