Consider the function fx x3x43 Determine whether the graph t

Consider the function f(x)= (x-3)(x+4)^3. Determine whether the graph touches the x-axis or crosses the x-axis at x=3.

Solution

f(x) = (x-3)(x+4)^2

Graph touches x axis when f(x) =0

(x-3)(x+4)^2=0

(x-3) =0 ; x=3

Graph crosses x axis at x= 3 ( as it is non- repeated root)

(x+4)^2 =0 ; x= -4,-4

Now repeated root at x = -4 . So, Graph touches x axis at x=-4