Search results
Results from the WOW.Com Content Network
The sum of two concave functions is itself concave and so is the pointwise minimum of two concave functions, i.e. the set of concave functions on a given domain form a semifield. Near a strict local maximum in the interior of the domain of a function, the function must be concave; as a partial converse, if the derivative of a strictly concave ...
The term convex is often referred to as convex down or concave upward, and the term concave is often referred as concave down or convex upward. [3] [4] [5] If the term "convex" is used without an "up" or "down" keyword, then it refers strictly to a cup shaped graph .
A related but distinct use of second derivatives is to determine whether a function is concave up or concave down at a point. It does not, however, provide information about inflection points . Specifically, a twice-differentiable function f is concave up if f ″ ( x ) > 0 {\displaystyle f''(x)>0} and concave down if f ″ ( x ) < 0 ...
If the second derivative of a function changes sign, the graph of the function will switch from concave down to concave up, or vice versa. A point where this occurs is called an inflection point. Assuming the second derivative is continuous, it must take a value of zero at any inflection point, although not every point where the second ...
This can also be seen from the geometric picture: the trapezoids include all of the area under the curve and extend over it. Similarly, a concave-down function yields an underestimate because area is unaccounted for under the curve, but none is counted above. If the interval of the integral being approximated includes an inflection point, the ...
The east north up (ENU) local tangent plane is similar to NED, except for swapping 'down' for 'up' and x for y. Local tangent plane coordinates (LTP) are part of a spatial reference system based on the tangent plane defined by the local vertical direction and the Earth's axis of rotation.
A: The bottom of a concave meniscus. B: The top of a convex meniscus. In physics (particularly fluid statics), the meniscus (pl.: menisci, from Greek 'crescent') is the curve in the upper surface of a liquid close to the surface of the container or another object, produced by surface tension.
If is concave down in the interval between and , the approximation will be an overestimate (since the derivative is decreasing in that interval). If is concave up, the approximation will be an underestimate. [1]