what is the the derivative of the absolute value fuction x-3
To find the derivative of the absolute value function f(x) = |x - 3|, we need to account for the fact that the derivative of the absolute value function is different for x > 3 and x < 3.
For x > 3:
We can rewrite f(x) = |x - 3| as f(x) = x - 3, since (x - 3) is already positive for x > 3. The derivative of f(x) = x - 3 is simply 1, since the derivative of any constant (in this case, -3) is zero.
For x < 3:
We can rewrite f(x) = |x - 3| as f(x) = -(x - 3), since (x - 3) is negative for x < 3. The negative sign is necessary to obtain the absolute value of a negative number. The derivative of f(x) = -(x - 3) is simply -1, again due to the derivative of a constant.
In summary, the derivative of the absolute value function f(x) = |x - 3| is:
1 for x > 3
-1 for x < 3