Using Graph of Function

[nycmath]

Precalculus
Michael Sullivan
Edition 10
Chapter 2, Section 2.3

Use the graph of the function f given

14. Is f decreasing on the interval (-8, -4)?

At the point (-8, -4), the function f is neither increasing or decreasing.

16. Is f decreasing on the interval (2, 5)?

Yes.

18. List the intervals on which f is decreasing.

(-10, -8), (-2, 0), (2, 5)

I want someone here to do 20, 22, and 24.

20.Is there a local maximum at 5? If yes, what is it?

22. List the number(s) at which f has a local minimum. What are the local minimum values?

24. Find the absolute maximum of f on [-10, 7].

[Eigenvalue]

20. No. There is a local minimum at x=5

22. There is a local minimum at -8, 0, and 5. The absolute minimum values are -4 and 0.

24. The absolute maximum value is 10, at x=2

[nycmath]

20. No. There is a local minimum at x=5

22. There is a local minimum at -8, 0, and 5. The absolute minimum values are -4 and 0.

24. The absolute maximum value is 10, at x=2

It's interesting to know how many questions can be developed from just one graph of f.

[Eigenvalue]

We can use Lagrange polynomial method to find the polynomial given some points

Just be looking at the graph, we know that the function will be divisible by x(x+10)(x²-25), as the function has (at least; the function does have other roots) roots (0,0) (-10,0) (5,0) and (-5,0).

[nycmath]

We can use Lagrange polynomial method to find the polynomial given some points

Just be looking at the graph, we know that the function will be divisible by x(x+10)(x²-25), as the function has (at least; the function does have other roots) roots (0,0) (-10,0) (5,0) and (-5,0).

I am not familiar with the Lagrange Polynomial Method. This must be some advanced form not taught in precalculus.