Given the function fx x4 9x3 4x2 36x Describe the end be

Given the function f(x) = x^4 - 9x^3 - 4x^2 + 36x Describe the end behavior of the graph of f(x). described the end behavior like this: f(x) rightarrow + infinity, as x rightarrow - infinity f(x) rightarrow +infinity, as x rightarrow + infinity

Solution

f(x) = x³(x-9) -4x(x-9)

= (x³-4x) (x-9)

= x(x²-4) ( x-9)

= ( x²-4) ( x²-9x)   

both the factors are quadratic factor with the leading term 1 (positive )

when x -> + infinity or - infinity x²-4 and x²-9x -> infinity and hence the the product

when x- > - inf f(x) -> + inf

when x- > + inf f(x) -> + inf