Question

f(x)= -x(x-2)^2(x+4)(x-6) answer the following questions.
1. What is the minimum number of roots?
2. Will it start and end in the same or different
directions?
3. Sketch your function.

Answer 1

For the given function f(x),

Minimum number of roots is 5

Graph will start and end in different directions

The graph is attached below

Given :

Function $f(x)= -x(x-2)^2(x+4)(x-6)$

We need to find the minimum number of roots

To find out the minimum number of roots we look at the degree of the given function

$-x(x-2)^2(x+4)(x-6\\x \cdot x^2 \cdot x \cdot x =x^5$

Minimum number of roots is 5

We know that the degree of the given function is also 5 that is odd

Leading coefficient is negative because we have -x

when the degree is odd and leading coefficient is negative then graph goes up on the left and goes down on the right

As x-> - ∞, f(x)-> ∞

As x-> ∞, f(x)-> -∞

Graph will start and end in different directions

Now we sketch the graph

The graph is attached below .

Learn more : brainly.com/question/11747044