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Lachlan1996
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given that f(x) = ax^3 + bx^2, f(2)=4 and f'(3)=99 find f(x), f(3) and f'(2)
 2 years ago
 2 years ago
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)
 2 years ago
 2 years ago

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Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
i cant find a way to isolate a or b to solve
 2 years ago

tjones89 Group TitleBest ResponseYou've already chosen the best response.0
have you found the derivative?
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
the derivative is 3ax^2 + 2bx but that doesnt help solve it
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
f(x) = ax^3 + bx^2 f(2) = 8a + 4b = 4 f(3) = 27a + 9b = 99
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
8a + 4b = 4 27a+9b=99 from equation 1 , we have : a = \(\LARGE\frac{44b}{8}=\frac{1b}{2}\) put this value in the second equation.
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
Can you now solve for a, b ? @Lachlan1996
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
wait wait, hold on youve lost me here.
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
lol, take your time. Sorry :)
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
uhhh i got 27a + 6b =99 but that is the gradient as in the derivative
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
so i dont think you can simultaneously solve it
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
because you are simultaneously solving a derivative and a point
 2 years ago

EulerGroupie Group TitleBest ResponseYou've already chosen the best response.1
Yes! Now use the f(2)=4 in the original equation to get your second equation with the two unknowns... a and b
 2 years ago

EulerGroupie Group TitleBest ResponseYou've already chosen the best response.1
Two equations with two unknowns should be solvable. Pick your favorite method for solving systems... @mathslover is using substitution.
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
but he is solving a f' (x) with a f (x)
 2 years ago

EulerGroupie Group TitleBest ResponseYou've already chosen the best response.1
a and b will be the same in the original and the derivative
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
ah yes i see
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
f(2) = 8a + 4b = 4 f(3) = 27a + 9b = 99 a = (1b)/2 put this in f(3) equation. 27(1b)/2 + 9b = 99 (2727b+18b)=198 27 9b = 198 9b = 198+27 = 225 b = 225/9 b = 25 You can solve for a now.
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
in the above equation isnt it meant to be 6a not 9a though?
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
wait no i mean 6b not 9b
 2 years ago

EulerGroupie Group TitleBest ResponseYou've already chosen the best response.1
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
 2 years ago

EulerGroupie Group TitleBest ResponseYou've already chosen the best response.1
27a+6b=99 8a+ 4b=4
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
uhh okie doke so a=0.5b0.5
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
however substituting that into 27a + 6b = 99 i got 8.333333 as being b
 2 years ago

EulerGroupie Group TitleBest ResponseYou've already chosen the best response.1
I got a=7, b=15
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
oh no made an error forgot to subtract 6b
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
OH MY FAULT , sorry :(
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
no, no it was a simple mistake, i just wasnt sure if you had made a mistake or were doing something else
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
this seems like alot of work just to start off the question, do you think this would be in an exam?
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
Depends but I do think, Yep! :)
 2 years ago

EulerGroupie Group TitleBest ResponseYou've already chosen the best response.1
For calculus, it doesn't seem out of bounds for a test.
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
ahh god, in a year 11 maths exam? i think im buggered then
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
Whether it will come or not in exam but I think you must be PREPARED
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
mmm yes my exam is in 5 weeks.
 2 years ago

EulerGroupie Group TitleBest ResponseYou've already chosen the best response.1
Creating a small system and solving it with substitution is fairly standard in calculus.
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
You have much time for it, go through these type of questions and ask your problems here...
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
okie doke, thanks very much for the help mate, its much appreciated. thankyou to you both
 2 years ago

EulerGroupie Group TitleBest ResponseYou've already chosen the best response.1
You're welcome.
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
Welcome! :)
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
uhhhh small problem
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
we got the answer wrong? its meant to be y=7x^3 15x^2
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
Try to do it again, I think calculation mistake?
 2 years ago

EulerGroupie Group TitleBest ResponseYou've already chosen the best response.1
yes... a=7, b= 15
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
ah yes, last step of my working didnt put the ve in the 15
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
hmn, Take care of these small mistakes .
 2 years ago

EulerGroupie Group TitleBest ResponseYou've already chosen the best response.1
whew! you scared me ;)
 2 years ago

Lachlan1996 Group TitleBest ResponseYou've already chosen the best response.0
will do, doesnt help when you get frustrated but. maths is not easy for me
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.0
I think it is f'(3)=99 not f(3)=99
 2 years ago
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