Give me the points of f(x)=-2|x+1|+1. Determine whether the function has its minimum or maximum values so you can place your first point there
To determine the points of the function f(x) = -2|x+1| + 1, we first need to find the critical points where the function may have its maximum or minimum values.
To find the critical points, we set the derivative of the function equal to 0 and solve for x:
f'(x) = 0
-2 * sign(x+1) = 0
sign(x+1) = 0
x+1 = 0
x = -1
Therefore, the critical point is x = -1.
To determine whether the function has its maximum or minimum value at x = -1, we can analyze the behavior of the function around this point.
For x < -1, the function becomes f(x) = -2(-x-1) + 1 = 2x - 1
For x > -1, the function becomes f(x) = -2(x+1) + 1 = -2x - 1
Since the coefficient of x is positive for x < -1 and negative for x > -1, the function has a minimum value at x = -1.
Therefore, the minimum point of the function f(x) = -2|x+1| + 1 is at (-1, -1).