Personally, I'd do those backwards from c, and I was taught to sketch graphs using a different method, so maybe someone else will be more in tune with your text. Anyway, following these steps:
a) Start with a table of values. This function is most interesting in x [-3, 3], so create a table of values of y given x:
f(-2) =(-2)^2-a(-2)^2+6
f(-1) =
f(0) =
f(1) =
f(2) =
f(3) =
Extend a few more values between or beyond, to taste.
b) Where does the function cross the x-axis? That is, where does it cross from negative to positive or vice-versa? If it's positive at 2 but negative at three you know you have (at least) one real root between.
c. The actual answer to this is to differentiate the function, and find where the derivative is zero.
f'(x)=3x^2-4x at zero,
3x^2 = 4x, which is true at x=0 and at x=4/3, so these points are going to be especially interesting.
I am very confused on how to graph Polynomial Functions and how to determine the extra stuff my HW is asking.
a. Graph each function by making a table of values.
b. Determine consecutive values of x between which each real zero is located.
c. Estimate the x-coordinates at which the relative maxima and relative minima occur.
problem-
f(x)=x(cubed)-2x(squared)+ 6
Just take the first one I have to do and please help me understand how to do this and what all this means!! Thanks!
-JAKE
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