Assignment Task

Introduction to differential calculus

Understanding differentiation is fundamental in mathematics, providing the groundwork for optimization, particularly in determining maximums and minimums. Graphical representation simplifies the intuition behind differentiation, where the slope (or gradient) of a straight line is defined as the change in y divided by the corresponding change in x. However, it`s important to note that the gradient varies with x, indicating a variable slope. In mathematical terms, if y = f(x), then the slope is represented by the derivative, denoted as f’(x) or "f dashed of x". Moving along a curve from a point (x, f(x)) to a nearby point (x+∆x, f(x+∆x)), the slope of the line connecting these points is calculated as (f(x+∆x)-f(x))/∆x. As ∆x approaches 0, this line`s slope approaches the slope of the tangent.

Applications of marginal analysis

Marginal analysis finds numerous applications in Economics and Finance, such as:

• Decision-making by monopolists and perfect competitors based on marginal costs and revenues
• Firms determining employment levels by examining the marginal product of labor
• Understanding marginal propensity to consume/save

Activity

Identify the x and y coordinates and categorize the stationary points of the function:

y = x³ + 4x² – 3x – 10

The form of the final assessment

Practical skills constitute 70% of the module mark, emphasizing comprehension rather than mere calculations. The assessment comprises four tasks, each carrying a 25% weighting, with two tasks focusing on econometrics and two on mathematical skills.