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Lachlan1996 Group Title given that f(x) = ax^3 + bx^2, f(2)=-4 and f'(3)=99 find f(x), f(3) and f'(2) one year ago one year ago

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1. Lachlan1996 Group Title

i cant find a way to isolate a or b to solve

2. tjones89 Group Title

have you found the derivative?

3. Lachlan1996 Group Title

the derivative is 3ax^2 + 2bx but that doesnt help solve it

4. mathslover Group Title

f(x) = ax^3 + bx^2 f(2) = 8a + 4b = -4 f(3) = 27a + 9b = 99

5. mathslover Group Title

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 Group Title

Can you now solve for a, b ? @Lachlan1996

7. Lachlan1996 Group Title

wait wait, hold on youve lost me here.

8. mathslover Group Title

lol, take your time. Sorry :)

9. Lachlan1996 Group Title

uhhh i got 27a + 6b =99 but that is the gradient as in the derivative

10. Lachlan1996 Group Title

so i dont think you can simultaneously solve it

11. Lachlan1996 Group Title

because you are simultaneously solving a derivative and a point

12. EulerGroupie Group Title

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 Group Title

Two equations with two unknowns should be solvable. Pick your favorite method for solving systems... @mathslover is using substitution.

14. Lachlan1996 Group Title

but he is solving a f' (x) with a f (x)

15. EulerGroupie Group Title

a and b will be the same in the original and the derivative

16. Lachlan1996 Group Title

ah yes i see

17. mathslover Group Title

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 Group Title

in the above equation isnt it meant to be 6a not 9a though?

19. Lachlan1996 Group Title

wait no i mean 6b not 9b

20. EulerGroupie Group Title

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 Group Title

27a+6b=99 8a+ 4b=-4

22. Lachlan1996 Group Title

uhh okie doke so a=0.5b-0.5

23. Lachlan1996 Group Title

however substituting that into 27a + 6b = 99 i got 8.333333 as being b

24. EulerGroupie Group Title

I got a=7, b=-15

25. Lachlan1996 Group Title

oh no made an error forgot to subtract 6b

26. mathslover Group Title

OH MY FAULT , sorry :(

27. Lachlan1996 Group Title

no, no it was a simple mistake, i just wasnt sure if you had made a mistake or were doing something else

28. Lachlan1996 Group Title

this seems like alot of work just to start off the question, do you think this would be in an exam?

29. mathslover Group Title

Depends but I do think, Yep! :)

30. EulerGroupie Group Title

For calculus, it doesn't seem out of bounds for a test.

31. Lachlan1996 Group Title

ahh god, in a year 11 maths exam? i think im buggered then

32. mathslover Group Title

Whether it will come or not in exam but I think you must be PREPARED

33. Lachlan1996 Group Title

mmm yes my exam is in 5 weeks.

34. EulerGroupie Group Title

Creating a small system and solving it with substitution is fairly standard in calculus.

35. mathslover Group Title

You have much time for it, go through these type of questions and ask your problems here...

36. Lachlan1996 Group Title

okie doke, thanks very much for the help mate, its much appreciated. thankyou to you both

37. EulerGroupie Group Title

You're welcome.

38. mathslover Group Title

Welcome! :)

39. Lachlan1996 Group Title

uhhhh small problem

40. Lachlan1996 Group Title

we got the answer wrong? its meant to be y=7x^3 -15x^2

41. mathslover Group Title

Try to do it again, I think calculation mistake?

42. EulerGroupie Group Title

yes... a=7, b= -15

43. Lachlan1996 Group Title

ah yes, last step of my working didnt put the -ve in the 15

44. mathslover Group Title

hmn, Take care of these small mistakes .

45. EulerGroupie Group Title

whew! you scared me ;)

46. Lachlan1996 Group Title

will do, doesnt help when you get frustrated but. maths is not easy for me

47. sauravshakya Group Title

I think it is f'(3)=99 not f(3)=99