Find the power function that the graph of fx x x2 x 1 resemb

Find the power function that the graph of f(x) x (x+2) (x -1) resembles for large values of lx

Solution

f(x) = - x²(x + 2)² (x² - 1)

as x is very large value x + 2 x , x² - 1 x²

==> f(x) = - x²(x + 2)² (x² - 1) - x² (x)² (x²)

==> f(x) - x⁶

Hence power function that the graph of f(x) resembles = -x⁶