I have been trying all day and I haven't been able to figure this homework problem out. Math is my weakest area. Can someone help me figure it out and maybe tell me how to do it? I would really appreciate it
1. Sketch a graph of the function: f(x) = 3x-2/√x^3+8
x cubed plus 8 is all under the radical
Find the function's domain and range
I really have big problems with finding domain and range. Will someone tell me what the domain and range is and how they got their answer?? Also, someone told me to use a graphic calculator to graph this but he told us not to and I don't know how to do it anyway. AHH. Help. Homework is due tomorrow and this is the only problem I have left. I really need a good grade or my school won't let me continue this program.
Here is the graph.
Let us assume the max point is . Then the range is . The problem is that that point is not 1, and I do not know how you are asked to find this. If this is a Calculus problem I can show you but it seems to not and hence it would be useless for me to explain.
The way to get the range is to find the maximum point for that curve, but I do not think the person who is asking knows Calculus. I have another way but it realies on the properties of a cubic, again I do not think he is supposed to know that either.
As this clearly goes to 0, and it is also well
behaved down to the bottom end of its domain where it goes to -infinity.
Therefore is has a calculus type maximum somewere in
So we differentiate and set the derivative equal to zero and solve to find the corresponding to the maxima.
Setting this equal to zero and simplifying gives:
Sketching this we see that it has one real root near .
Formula itteration of:
refines the root to , so the maximum of is . (If we wish the exact root we would use the cubic formula to find it in closed from)
Hence the range is .
(note if we had the exact maxima the function achives its maxima that is why I have used a ] closing bracket)