calculus
posted by Matt .
I need to find the critical number of 4x^336x^2+96x64 by factoring. Basically I need to know the zeros.

If you plug in x=1, you find that f(x)=4x^336x^2+96x64 evaluates to zero. From here, use either synthetic division or long division to get the quadratic 4x^232x+64. Reduce to x^28x+16 and solve by factoring into (x4)^2.
So 4x^336x^2+96x64=4(x1)(x4)^2. 
The critical numbers are the values for x in which the function has a horizontal tangent line, so where the first derivative is zero.
F1(x)=12x^272x+96
0=12x^272x+96
0= x^26x+8
0=(x4)(x2)
The critical numbers are
x=4 and x=2 
If you need to find the zeros of a cubic by factoring then the resault is:
4(x4)^2(x1), so the zeros are at 4, and 1, and these are also the critical points.
You did not specify if 4x^336x^2+96x64 was your function, or the first derivative of the function, however if it is not then you should take the first derivative which should leave you a quadratic function, then use the quadratic formula on the remaining seconddegree polynomial. 
Well, everything divides by 4, so you can take that out for a start, leaving
x^3  9x^2 + 24x  16
We need three numbers with a product of 16 (1, 2, 4, 8 and 16 are the only possibilities) that sum to 9.
Shouldn't be too hard to figure out from there.
Respond to this Question
Similar Questions

derivative am i right or wrong
what is the antiderivative of 1/(x^22x+2)? 
mathcalc
f(x)=2x^336x^2+162x6 small critical number? 
algebra
Completely factor the expression. 36x^3 96x^2y+64xy^2 
Calculus
Find the Critical Numbers? 1.) f(x) = 2x^3 + 3x^2 + 36x x=? 
college allgebra
f(x)=x^6+4x^5+4x^4+3x^3x^25x+4 Find the maximum number of real zeros, and Use Descartes's rule of signs to determine how many positive and how many negative zeros the function has. You do not need to find the zeros. 
calculus
For the following function f(x)=2x^46x^2+2x1. Find the maximum number of real zeros and Use Descartes's rule of signs to determine how many positive and how many negative zeros the function has. You do not need to find the zeros. 
Calculus
What are the critical numbers of the function: f(x)=2x^33x^236x+14 Thanks 
Calculus
I'm doing test corrections, and it's been a few weeks since we did this, so I'm a little fuzzy. I'm supposed to find the zeros, relative extrema, and inflection points of f(x) = x^3  6x^2 + 3x + 10. The zeros would be 1, 2, and 5 … 
Math College Algebra
Find the zeros of the following USE ALL THE THREE METHODS FOR EACH NUMBER ( Factoring, Completing the Squares and Quadratic Formula) 1.f(x) =3x+5 2.g(y)=y^23y+2 3.s(xl= 6x^213x+5 Please help me I need this before 2 hours to come. … 
Math College Algebra (urgent before 2hours)
Find the zeros of the following USE ALL THE THREE METHODS FOR EACH NUMBER ( Factoring, Completing the Squares and Quadratic Formula) 1.f(x) =3x+5 2.g(y)=y^23y+2 3.s(xl= 6x^213x+5 Please help me I need this before 2 hours to come. …