What happens when you take the derivative of x?

When x is substituted into the derivative, the result is the slope of the original function y = f (x). There are many different ways to indicate the operation of differentiation, also known as finding or taking the derivative.

What is the derivative when x 0?

You know that f(x)=0 is a constant function. Thus its derivative is zero.

Is the derivative change in y over change in x?

Another name for the steepness of a straight line is SLOPE. Slope is defined as the change in y divided by the change in x. The slope of the function y=f(x) at the point “x” is called the DERIVATIVE.

What does it mean when the derivative of a function is zero?

The derivative of a function, f(x) being zero at a point, p means that p is a stationary point. That is, not “moving” (rate of change is 0). There are a few things that could happen. Either the function has a local maximum, minimum, or saddle point.

Can you have a derivative of 0?

Answer and Explanation: The derivative of 0 is 0. In general, we have the following rule for finding the derivative of a constant function, f(x) = a.

What is the derivative of f/x at x 0?

Hence, the derivative of |x| at x = 0 does not exist.

How do you change the derivative of a zero?

Find the first derivative of f using the power rule. Set the derivative equal to zero and solve for x….Here’s how:

1. Take a number line and put down the critical numbers you have found: 0, –2, and 2.
2. Pick a value from each region, plug it into the first derivative, and note whether your result is positive or negative.

What does taking a derivative mean?

In summary, the derivative is basically the slope, or instantaneous rate of change, of the tangent line. at any point on the curve. When you take the derivative of a function, you end up. with another function that provides the slope of the original function.