Question

(2/4x)^(4)+(10/3x)^(3)+(-32/2x)^(2)-160x find the critical points

Answer 1

critical points are any points where: the derivative of your function = 0, or do not exist
and also exist inside the domain of your original function

Answer 2

i took the derivative and got 2x^3+10x^2-32x-160 now i just set that equal to zero to find the critical points?

Answer 3

yep, since you have a polynomial function, that means there are no points on your derivative where the derivative does not exist (it's continous and differentiable along the entire domain)

that leaves the other condition: setting your derivative = 0 and solving for the critical points.

once you are done with that, you need to make sure that the all the critical points you find exist in the domain of your original function. (i.e., you don't get errors if you plug them in to your function f(x) )

Answer 4

i got -5,-4,and 4

Answer 5

plug it into the original funtion to see if it is a max or min right?

Answer 6

that is one way to do it