Expert: Scotto - 6/13/2008

Question
how do i determine the x and y intercepts of the function to being the rest of this curve sketching problem?
y= 3x2-1/X3 the numbers after the x's are the square and cube. i think i will be fine with the rest of this assighnment but i just need help getting started.

Answer
The way that most people have learned to write the function (for future use) is y = 3x^2-1/x^3.  The sketch resembles the parbola 3x^2 since 1/x^3 quickly goes to 0 as |x| increases.

Near (0,0), however, the function increases on the negative side and decreases on the positive side.  At -.01, for instance, the function is 1,000,000 and at 0.01, the function is -1,000,000.  Note that the 3x^2 only has the value 0.0003 at this point which is far outweighed by the -1/x^3 when anywhere close to 0.

At x=0 the function is undefined and has no limit.  The root can be found using the bisection method near 0.8.

The binomial is to let x1=0.7, x2=0.9, and then x3=(x1+x2) over 2.  Replace x1 or x2 with x3 depending on which one has the same sign in the f(x) value.  Note that the (0.7+0.9)/2=0.8 replaces the 0.7 since f(0.8)=-0.033125.  Next we get (0.8+0.9)=0.85 with f(0.85)=0.539167, so the 0.85 replace the 0.9.  Our two x values are now 0.8 and 0.85.  You can proceed as far as you need to.  I did it on the computer in Excel.  I copied the value in A3 to A2 or A1, depending on the sign of the number.