- #1
Ali Asadullah
- 99
- 0
What is Cusp and what are the values of derivatives on left and right side of it?
A cusp is a point on a curve where the curve changes direction abruptly and is not smooth. It can occur in a graph when the slope of the curve changes rapidly at a specific point.
The value of a derivative at a cusp can be determined by taking the limit of the derivative as it approaches the point of the cusp. This can be calculated using the left-hand and right-hand limits of the derivative at the cusp point.
Yes, a function can have a cusp at a specific point and still be continuous. This occurs when the left-hand and right-hand limits of the function at the cusp point are equal.
A cusp is significant in calculus because it represents a point of non-differentiability. This means that the function is not smooth at the cusp point and the derivative does not exist at that point.
To graph a function with a cusp, you can plot the points around the cusp and connect them with a smooth curve. It is also helpful to determine the slope of the curve on either side of the cusp to accurately represent the steepness of the curve at that point.