Question

How do you do this question?

Answer 1

Answer:

Step-by-step explanation:

In order to answer this question, you need to be able to reproduce the general shape of this curve. It takes a bit of doing but here is one solution

y = x(x + 1)^3 * (x - 2)(x - 1)^2

1. So here are the critical parts of the shape. At - 1 there is a slide that is taking place across the x axis. (x + 1)^3 is responsible for this.
2. It is coming from below the x axis on the left. The whole equation is responsible for that.
3. There is a local maximum next which falls to 0,0 (on my graph). It dips down (if you look carefully at your graph and touches the x axis from below.  My graph exaggerates this.
4. Finally this is a local just before 2.

I have not discovered what the exact equation you were given was. But when I have the shape, I can check off the characteristics that are true.

The minimum number of x's in this is 7. That's true.

The graph has only 2 relative minima. Not 3. So that's false. Don't check it.

The constant term of the graph is not 4. You can tell that by looking at your graph. The constant term is the y intercept. It looks to me like it is 0. This statement is false.

The minimum degree is 7 not 5. False

The minimum degree is 7 not 6. False

The leading coefficient is not negative. This statement is false. When you multiply this out, you get an ax^7 where a>0.

Your graph has 1 local  and one global maximum. I'm not sure how you count that. I guess it is true.

My graph has 5 turning points (I think). I think yours does too. Yours is hard to tell on this issue, but I'm pretty sure it's true. a turning point is one where the direction changes. When you hit a maximum (or minimum) you also hit a turning point. This statement is true.

The leading coefficient is plus. That's true.

The last point is true. It has one global maximum on the right. The other maximum is a local maximum.