If the even function f (x) is an increasing function in the interval [3,7], and the maximum value is 5, then f (x) is an increasing function in the interval [- 3, - 7]

If the even function f (x) is an increasing function in the interval [3,7], and the maximum value is 5, then f (x) is an increasing function in the interval [- 3, - 7]

The maximum value is 5

The even function f (x) is a decreasing function in the interval [1,3] and has a minimum value of - 1. F (x) is a decreasing function in the interval [- 3, - 1]
A minus function and maximum value - 1 b minus function and minimum value - 1 C increasing function and maximum value - 1 D increasing function and minimum value - 1 need detailed process solution, thank you

A:
The even function f (x) is a decreasing function on [1,3], which has a minimum value of - 1, and the minimum value of - 1 is obtained at x = 3
If f (x) is an increasing function in the interval [- 3, - 1], it has a minimum value of - 1, and the minimum value of - 1 is obtained at x = - 3
So: choose D
This topic investigates the knowledge points of even function about Y-axis symmetry

If f (x) = AX3 + BX (a is not equal to 0), the tangent slope at (1, f (1)) is - 6, and the minimum value of derivative function is - 12

The derivative is f '(x) = 3ax2 B, f' (1) = 3AB = - 6
The minimum value of F '(x) is B, so B = - 12, and the solution is a = 2