Question

Graph y = x3 – 4x2 + 6. Describe what you see

Answer 1

The way your computer or graphing calculator is going to do this is simply input values for x into a table with outputs for y and then connect the dots.

In this case, the first thing to check (if you're having to do it by hand) is if it factors. If it does then you can find the roots (where the graph will go across the x-axis, on the xy-plane)

Sadly it doesn't factor nicely here.

But you can use some calculus if you want to find something about the shape. Are you familiar with calculus?

Answer 2

It's a x\(^3\) type of function, x-cubed, so that means you're going to have some sort of an "S" shape to it.

When the first derivative of this function is zero, when y'=0, that's when your slope is zero and where you're going to have minimums and maximum points.

If the second derivative is positive (y">0) then you have a local minimum.
If the second derivative is negative (y"<0) then you have a local maximum.

When the second derivative is zero, that's when you're going to have an "inflection point", where the original function's graph curves upward or downward.



Make sense @simplybeyoutiful ?