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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)
 one year ago
 one year ago
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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Lachlan1996Best ResponseYou've already chosen the best response.0
i cant find a way to isolate a or b to solve
 one year ago

tjones89Best ResponseYou've already chosen the best response.0
have you found the derivative?
 one year ago

Lachlan1996Best ResponseYou've already chosen the best response.0
the derivative is 3ax^2 + 2bx but that doesnt help solve it
 one year ago

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

mathsloverBest 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.
 one year ago

mathsloverBest ResponseYou've already chosen the best response.2
Can you now solve for a, b ? @Lachlan1996
 one year ago

Lachlan1996Best ResponseYou've already chosen the best response.0
wait wait, hold on youve lost me here.
 one year ago

mathsloverBest ResponseYou've already chosen the best response.2
lol, take your time. Sorry :)
 one year ago

Lachlan1996Best ResponseYou've already chosen the best response.0
uhhh i got 27a + 6b =99 but that is the gradient as in the derivative
 one year ago

Lachlan1996Best ResponseYou've already chosen the best response.0
so i dont think you can simultaneously solve it
 one year ago

Lachlan1996Best ResponseYou've already chosen the best response.0
because you are simultaneously solving a derivative and a point
 one year ago

EulerGroupieBest 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
 one year ago

EulerGroupieBest 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.
 one year ago

Lachlan1996Best ResponseYou've already chosen the best response.0
but he is solving a f' (x) with a f (x)
 one year ago

EulerGroupieBest ResponseYou've already chosen the best response.1
a and b will be the same in the original and the derivative
 one year ago

mathsloverBest 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.
 one year ago

Lachlan1996Best ResponseYou've already chosen the best response.0
in the above equation isnt it meant to be 6a not 9a though?
 one year ago

Lachlan1996Best ResponseYou've already chosen the best response.0
wait no i mean 6b not 9b
 one year ago

EulerGroupieBest 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
 one year ago

EulerGroupieBest ResponseYou've already chosen the best response.1
27a+6b=99 8a+ 4b=4
 one year ago

Lachlan1996Best ResponseYou've already chosen the best response.0
uhh okie doke so a=0.5b0.5
 one year ago

Lachlan1996Best ResponseYou've already chosen the best response.0
however substituting that into 27a + 6b = 99 i got 8.333333 as being b
 one year ago

Lachlan1996Best ResponseYou've already chosen the best response.0
oh no made an error forgot to subtract 6b
 one year ago

mathsloverBest ResponseYou've already chosen the best response.2
OH MY FAULT , sorry :(
 one year ago

Lachlan1996Best 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
 one year ago

Lachlan1996Best 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?
 one year ago

mathsloverBest ResponseYou've already chosen the best response.2
Depends but I do think, Yep! :)
 one year ago

EulerGroupieBest ResponseYou've already chosen the best response.1
For calculus, it doesn't seem out of bounds for a test.
 one year ago

Lachlan1996Best ResponseYou've already chosen the best response.0
ahh god, in a year 11 maths exam? i think im buggered then
 one year ago

mathsloverBest ResponseYou've already chosen the best response.2
Whether it will come or not in exam but I think you must be PREPARED
 one year ago

Lachlan1996Best ResponseYou've already chosen the best response.0
mmm yes my exam is in 5 weeks.
 one year ago

EulerGroupieBest ResponseYou've already chosen the best response.1
Creating a small system and solving it with substitution is fairly standard in calculus.
 one year ago

mathsloverBest 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...
 one year ago

Lachlan1996Best ResponseYou've already chosen the best response.0
okie doke, thanks very much for the help mate, its much appreciated. thankyou to you both
 one year ago

Lachlan1996Best ResponseYou've already chosen the best response.0
uhhhh small problem
 one year ago

Lachlan1996Best ResponseYou've already chosen the best response.0
we got the answer wrong? its meant to be y=7x^3 15x^2
 one year ago

mathsloverBest ResponseYou've already chosen the best response.2
Try to do it again, I think calculation mistake?
 one year ago

EulerGroupieBest ResponseYou've already chosen the best response.1
yes... a=7, b= 15
 one year ago

Lachlan1996Best ResponseYou've already chosen the best response.0
ah yes, last step of my working didnt put the ve in the 15
 one year ago

mathsloverBest ResponseYou've already chosen the best response.2
hmn, Take care of these small mistakes .
 one year ago

EulerGroupieBest ResponseYou've already chosen the best response.1
whew! you scared me ;)
 one year ago

Lachlan1996Best ResponseYou've already chosen the best response.0
will do, doesnt help when you get frustrated but. maths is not easy for me
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.0
I think it is f'(3)=99 not f(3)=99
 one year ago
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