If an odd function has a maximum in [a, b], then the function has () A. Minimum B. maximum C. no maximum D. cannot be determined

If an odd function has a maximum in [a, b], then the function has () A. Minimum B. maximum C. no maximum D. cannot be determined

∵ the odd function has the maximum value in [a, b], and the function has the minimum value in [- B, - A]

If the even function f (x) has the maximum value 3 on [a, b], then the function has the maximum value 3 on [- B, - A]___ The value is______

Even function f (x) has a maximum value of 3 on [a, b]
=>f(b)=3
Function on [- B, - A]
f(-b)=f(b)=3
If the even function f (x) has the maximum value 3 on [a, b], then the function has the maximum value 3 on [- B, - A]_ Big__ The value is 3

If the even function f (x) has the maximum value on [a, b], then the function has no minimum value on [b, - A]
If the even function f (x) has the maximum value on [a, b], then the function is on [- B, - A]
A has no minimum B has no maximum C has a minimum D has a maximum

The function f (x) has a maximum value on [a, b], and there exists a x0 (constant), so that it has a maximum value for any x ∈ [a, b]
f(x)≤f(x0).①
Because f (x) is an even function;
So,
f(x)= f(-x)
f(x0)=f(-x0);
① The formula can be changed into:
f(-x)≤f(-x0)
And, - x0, - x ∈ [- B, - A]
Let t = - X
T0 = - x0 (constant),
That is to say, there exists a t0 ∈ [- B, - A]. For any t ∈ [- B, - A], f (T) ≤ f (T0),
Answer [D]