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The derivative at any point in a curve is equal to the slope of the line tangent to the curve at that point.

Doing it in terms of the actual expression of the curve, find the derivative of the curve, then plug the x-value of the point into the derivative to find the derivative at that point.

Q: What does the derivative at a point mean?

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the second derivative at an inflectiion point is zero

I am assuming the you are talking about the graph of the derivative. The graph of the derivative of F(x) is the graph such that, for any x, the value of x on the graph of the derivative of F(x) is the slope at point x in F(x).

The derivative of a curve is basically the slope of the curve. If we say, for example, that if y = 2x, the derivative is 2, that means that at any point the line has this slope. If we say that for the function y = x2, the derivative is 2x, that means that at any point "x", the slope is twice the value of "x".

point is also known as dot.

If the second derivative of a function is zero, then the function has a constant slope, and that function is linear. Therefore, any point that belongs to that function lies on a line.

Let f be a function and a be the given point you are considering. Then,f(x) - f(a)---------------(x-a)is the difference quotient. If the limit as x approaches a exists, then the function is differentiable at a, or we say the derivative exists at a. If that limit does not exist, then the derivative does not exist at that point.

This means that the function has reached a local maximum or minimum. Since the graph of the derivative crosses the x-axis, then this means the derivative is zero at the point of intersection. When a derivative is equal to zero then the function has reached a "flat" spot for that instant. If the graph of the derivative crosses from positive x to negative x, then this indicates a local maximum. Likewise, if the graph of the derivative crosses from negative x to positive x then this indicates a local minimum.

A function is differentiable at a point if the derivative exists there.

The slope of a curved line at a point is the slope of the tangent to the curve at that point. If you know the equation of the curve and the curve is well behaved, you can find the derivative of the equation of the curve. The value of the derivative, at the point in question, is the slope of the curved line at that point.

Finding the derivative. The derivative is the measure of how a function changes as its input changes.

the deivative of a function is the gradient, at a point if you can sub in the x coordinate for that point

For example, if the slope at a certain point is 1.5, you can draw a line that goes through the specified point, with that slope. The line would represent the slope at that point. If you want to graph the slope at ALL POINTS, take the derivative of the function, and graph the derivative. The derivative shows the slope of a function at all points.