Monday

April 21, 2014

April 21, 2014

Posted by **Matt** on Monday, November 9, 2009 at 1:25pm.

- calculus -
**Jeff**, Monday, November 9, 2009 at 5:43pmIf you plug in x=1, you find that f(x)=4x^3-36x^2+96x-64 evaluates to zero. From here, use either synthetic division or long division to get the quadratic 4x^2-32x+64. Reduce to x^2-8x+16 and solve by factoring into (x-4)^2.

So 4x^3-36x^2+96x-64=4(x-1)(x-4)^2.

- calculus -
**Thomas**, Monday, November 9, 2009 at 5:45pmThe 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^2-72x+96

0=12x^2-72x+96

0= x^2-6x+8

0=(x-4)(x-2)

The critical numbers are

x=4 and x=2

- calculus -
**Thomas Kilbride**, Monday, November 9, 2009 at 5:46pmIf you need to find the zeros of a cubic by factoring then the resault is:

4(x-4)^2-(x-1), so the zeros are at 4, and 1, and these are also the critical points.

You did not specify if 4x^3-36x^2+96x-64 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 second-degree polynomial.

- calculus -
**TeacherJim**, Monday, November 9, 2009 at 5:53pmWell, 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.

**Related Questions**

college allgebra - f(x)=x^6+4x^5+4x^4+3x^3-x^2-5x+4 Find the maximum number of ...

Calculus - Urgent!!! - In case this looks familiar, yes, it is a repost. I ...

calculus - For the following function f(x)=2x^4-6x^2+2x-1. Find the maximum ...

Algebra 2 - find all the zeros of the polynomial function F(x)= x^4+4x^3-6x^2-...

Calculus - I'm doing test corrections, and it's been a few weeks since we did ...

help please! - f(x)=x+1/x Find all critical numbers. Find where the function is ...

math-calc - f(x)=2x^3-36x^2+162x-6 small critical number? Large critical number?

Calculus - Find the Critical Numbers? 1.) f(x) = 2x^3 + 3x^2 + 36x x=? 2.) g(t...

derivative am i right or wrong - what is the antiderivative of 1/(x^2-2x+2)? ...

Algebra - Please help with this factoring problem: 2x^3/2 − 6x^1/2 + 4x^&#...