Question

() = ( − 312)^3( + 8900)( − 40800)^2 At which x-intercept(s) is the graph of f tangent to the x-axis, describe the end behavior

Answer 1

We have the following function:

`\mleft(\mright)=\mleft(-312\mright)^3\mleft(+8900\mright)\mleft(-40800\mright)^2`

as we can note the factor (x-40800) has a degree of 2, this means that the graph bounces off the x-axis

In other words, at x=40800 the graph of f(x) is tangent to the x-axis.

On the other hand, the total degree of the function f(x) is equal to 1+3+1+2=7 and the leading coefficient is positive, then f(x) has the following behavior:

`f(x)\approx x^7+.\ldots`

Then, function f(x) raises up as x becomes larger and falls as x becomes smaller: