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let f(x)=ax^3+6x^2+bx+4. Determine the constant a and b such that f has a relative min at x=1 and a rel max at x=2@Algebra
 2 years ago
 2 years ago
let f(x)=ax^3+6x^2+bx+4. Determine the constant a and b such that f has a relative min at x=1 and a rel max at x=2@Algebra
 2 years ago
 2 years ago

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moneybirdBest ResponseYou've already chosen the best response.2
first derivative of f(x) first
 2 years ago

giggles123Best ResponseYou've already chosen the best response.0
I did that then what? I got F'(x)=3ax^2+12x+b
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
\[f'(x)=3a^2+12x+b\] \[f'(1)=0 ;f'(2)=0\]
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
\[f'(x)=3ax^2+12x+b*\]
 2 years ago

HeroBest ResponseYou've already chosen the best response.0
I was just about to say....what happened to the x?
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
\[f'(2)=3a(4)+12(2)+b=0\]
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
\[3a+b=12\] \[12a+b=24\]
 2 years ago

moneybirdBest ResponseYou've already chosen the best response.2
3a + b =12 12a + 24 +b = 0 12a + b =24 (3a + b) = 12 9a = 36 a = 4 b =24
 2 years ago

giggles123Best ResponseYou've already chosen the best response.0
what happened to the x?
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
\[ 3a+b=12\] \[(12a+b=24)\]  9a+0b=36 9a=36 a=4 12+b=12 b=24 gj money
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
what do you mean what happen to x?
 2 years ago

giggles123Best ResponseYou've already chosen the best response.0
how did you go from f'(x)=3ax^2+12x+b* to f′(−1)=3a−12+b=0
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
\[f(a)=4x^3+6x^2+24x+4\]
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
1 and 2 are critical numbers this is a polynomial so our critical numbers only exist when f'=0
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
money and i applied these conditions to f'
 2 years ago

giggles123Best ResponseYou've already chosen the best response.0
I got it. Thank you so much!
 2 years ago

luckeyBest ResponseYou've already chosen the best response.0
here b can take any value and a is rrestricted to any value in the interval (2,2)
 2 years ago
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