ihavesquarebrain
Answered

Suppose a function has a local max of (-1, 3) what can you conclude if the function is even? what can you conclude if the function is odd?
Suppose your function is increasing from the interval [2,5] what can you conclude if the function is even? what can you conclude if it is odd?



Answer :

Using the concept of even and odd functions, it is found that, considering the function has a local max at (-1,3):

  • If the function is even, it will have another local max at (1,3).
  • If the function is odd, it will have a local min at (1,-3).

For a function increasing on [2,5], we have that:

  • If the function is even, it will be decreasing on [-5,-2].
  • If the function is odd, it will be increasing on [-5,-2].

What are even and odd functions?

  • In even functions, we have that f(x) = f(-x) for all values of x.
  • In odd functions, we have that f(-x) = -f(x) for all values of x.
  • If none of the above statements are true, the function is neither.

Hence, considering the function has a local max at (-1,3):

  • If the function is even, it will have another local max at (1,3).
  • If the function is odd, it will have a local min at (1,-3).

For a function increasing on [2,5], we have that:

  • If the function is even, it will be decreasing on [-5,-2].
  • If the function is odd, it will be increasing on [-5,-2].

For even functions it will decrease because we have that f(4) > f(3), for example, hence f(-4) > f(-3).

For the odd function it will increase because if f(4) > f(3), then f(-3) > f(-4) due to the negative signal.

More can be learned about even and odd functions at https://brainly.com/question/13048723

#SPJ1

Other Questions