I Need help finding the critical points for 11+30x+18x^2+2x^3. how do i factor wit 4 sets of numbers?
2007-10-23 16:20:41 · 3 answers · asked by sleepingdogslay 1 in Science & Mathematics ➔ Mathematics
find the first derivative of your problem, set them equal to 0 and then find the zeros...
f('x) = 30 + 32x + 6x^2
Thats your first derivative, set it equal to zero and then find the x intercepts..once you find that plug it back into the original equation to find the y, thats your critical points.
2007-10-23 16:32:54 · answer #1 · answered by Ge Y 2 · 0⤊ 0⤋
Finding the critical points means taking the derivative, and setting it equal to 0.
f ' =6x^2+36x+30=0
x^2+6x+5=0
(x+5)(x+1)=0
x=-5,-1
Plug these back in to get the y values:
f(-5)=2(5)^3+18(5)^2+30(5)+11
f(-1)=2(-1)^3+18(-1)^2+30(-1)+11
2007-10-23 23:34:19 · answer #2 · answered by Amelia 6 · 0⤊ 0⤋
The critical points happen only when the derivative is zero. The derivative, in this case is 30 + 36x + 6x^2. Since this must be zero at a critical point, you get a quadratic equation--which happens to have two distinct real roots. These are the x values of your critical points.
2007-10-23 23:35:18 · answer #3 · answered by husoski 7 · 0⤊ 0⤋