What is the second derivative called?
The second derivative is the rate of change of the rate of change of a point at a graph (the “slope of the slope” if you will).
How do you know if the second derivative is positive or negative?
The second derivative tells whether the curve is concave up or concave down at that point. If the second derivative is positive at a point, the graph is bending upwards at that point. Similarly if the second derivative is negative, the graph is concave down.
What happens when a double derivative is zero?
Since the second derivative is zero, the function is neither concave up nor concave down at x = 0. It could be still be a local maximum or a local minimum and it even could be an inflection point. Let’s test to see if it is an inflection point.
What does it mean when the second derivative is zero?
3. The second derivative is zero (f (x) = 0): When the second derivative is zero, it corresponds to a possible inflection point. If the second derivative changes sign around the zero (from positive to negative, or negative to positive), then the point is an inflection point.
How do you tell if a critical point is a max or min?
Determine whether each of these critical points is the location of a maximum, minimum, or point of inflection. For each value, test an x-value slightly smaller and slightly larger than that x-value. If both are smaller than f(x), then it is a maximum. If both are larger than f(x), then it is a minimum.
What do critical points tell you?
A critical point is a point in the domain (so we know that f does have some value there) where one of the conditions: f'(c)=0 or f'(c) does not exist, is satisfied. If f has any relative extrema, they must occur at critical points.
What is supercritical condition?
When a compound is subjected to a pressure and a temperature higher than its critical point, the fluid is said to be ” supercritical ” . In the supercritical region, the fluid exhibits particular proporties and has an intermediate behavior between that of a liquid and a gas.