The derivative of an absolute value function is a piecewise function, where the derivative is -1 if the input is negative, 1 if the input is positive, and undefined at the point where the input is 0.
To find the derivative of a piecewise function with absolute value, you need to break the function into two separate cases: one for when the input is positive and one for when the input is negative. Then, you can use the power rule and chain rule to find the derivative for each case.
No, the derivative of an absolute value function is always either 1 or -1. This is because the derivative of an absolute value function is a piecewise function, and the derivative is defined as -1 for negative inputs and 1 for positive inputs.
The derivative of an absolute value function can help identify critical points, which are points where the slope of the function is 0. At these points, the derivative of the absolute value function is undefined. So, to find critical points, you can set the derivative equal to 0 and solve for the input value.
Yes, the derivative of an absolute value function can have a point of discontinuity. This occurs at the point where the input is 0, as the derivative is undefined at this point. This is because the derivative of an absolute value function is a piecewise function and is not continuous at the point where the input is 0.