Ana Sayfa » Anadolu Üniversitesi AÖF » İşletme Lisans Programı » Mathematics-1

Ünite 6: Derivative and İts Applications — Kavram Eşleştirme

Tur 1 / 30 / 5 eşleşti

Önce bir kavram seç, sonra karşılığı olan tanıma dokun.

Kavramlar

Tanımlar

Yukarıdan bir kavram seç.

Monotone Increasing — A function is monotone increasing on an interval if for any two points in the interval, a larger input always yields a larger output. This is guaranteed if the first derivative of the function is strictly positive throughout the interval.

Monotone Decreasing — A function is monotone decreasing on an interval if a larger input always yields a smaller output. This behavior occurs on intervals where the first derivative of the function is strictly negative.

Critical Point — A point in the domain of a differentiable function where the first derivative is equal to zero. These points are candidates for local maximum or local minimum values.

Sign Table — A tabular representation used to track the sign of the first derivative across different intervals determined by critical points. It helps visualize where the function is increasing, decreasing, and where its local extrema are located.

Optimization — The mathematical process of finding the maximum or minimum value of a function. In practical scenarios, it is used to maximize areas, revenues, and profits, or to minimize costs and materials.

Ceteris Paribus — A Latin phrase meaning 'holding other things constant'. In economics, it is used to isolate the relationship between two specific variables, such as price and demand, while assuming all other factors remain unchanged.

Demand Function — A mathematical relationship showing the quantity of a product that consumers are willing to buy at a given price. It typically has a negative slope, reflecting that lower prices increase demand.

Supply Function — A mathematical relationship showing the quantity of a product that producers are willing to sell at a given price. It typically has a positive slope, as higher prices encourage higher production.

Equilibrium Point — The intersection point of the supply and demand curves where the quantity supplied equals the quantity demanded. It determines the market price and is economically meaningful only when both coordinates are positive.

Break-Even Point — The level of production and sales where total revenue equals total cost. At this point, the business makes neither a profit nor a loss, and any sales beyond this point generate profit.

Marginal Cost — The derivative of the total cost function, representing the approximate additional cost incurred by producing one more unit of a good or service.

Marginal Revenue — The derivative of the total revenue function, representing the additional income generated by selling one more unit of a product.

Marginal Profit — The derivative of the total profit function, calculated as the difference between marginal revenue and marginal cost, representing the change in profit from a one-unit increase in sales.

Second Derivative Test — A method used to determine whether a critical point is a local maximum or minimum. If the first derivative is zero and the second derivative is negative, it is a local maximum; if positive, it is a local minimum.