Question

Найди наименьшее значение функции y=|x+3|-3 на отрезке [-2; 1]. помогите пожалуйста.

Answer 1

Ответ:

Y=(x+3) -3 

[2;1]

x^2 = 2*1-3

x^2 = 2

x=2*2

x=4

Answer 2

Finding the Minimum Value of the Function y = |x + 3| - 3 on the Interval [-2, 1]

To find the minimum value of the function y = |x + 3| - 3 on the interval [-2, 1], we need to evaluate the function at the endpoints and critical points within the interval.

Let's start by evaluating the function at the endpoints:

- When x = -2: - y = |-2 + 3| - 3 = |1| - 3 = 1 - 3 = -2

- When x = 1: - y = |1 + 3| - 3 = |4| - 3 = 4 - 3 = 1

Now, let's find the critical points by setting the derivative of the function equal to zero and solving for x:

- The derivative of y = |x + 3| - 3 is given by: - y' = (x + 3)/|x + 3|

To find the critical points, we need to solve the equation y' = 0:

- (x + 3)/|x + 3| = 0

Since the numerator (x + 3) cannot be zero, the only solution is when the denominator (|x + 3|) is zero. This occurs when x = -3.

Now, let's evaluate the function at x = -3:

- When x = -3: - y = |-3 + 3| - 3 = |0| - 3 = 0 - 3 = -3

To summarize the results:

- y(-2) = -2 - y(-3) = -3 - y(1) = 1

The minimum value of the function y = |x + 3| - 3 on the interval [-2, 1] is -3, which occurs at x = -3.

Note: The function y = |x + 3| - 3 is a piecewise function, where the expression inside the absolute value changes sign at x = -3. This results in a sharp corner or "kink" in the graph of the function at x = -3.