Mathematical Economics

Functions of one variable

(DEMO)

Reference book: Sydsaeter and Hammond

Play with Graphs- Arihant 

Content plan for Day 1:

Graphs of Functions: Special focus on trigonometric functions. All basic functions like exponential, logarithmic and power functions will be covered.

Linear and quadratic functions: Domain, Range, Notations, optimisation problems.

Functions:

Definition: A real valued function is a function that assigns a unique real number to a real variable x in the domain D. The set of values f(x) taken by x is called the range of f.

Quadratic Functions: A function from R-R(n) taking the form ax(n) + bx(n-1)+ ........ +z , where a,b,.....z belong to R and a is not equal to 0.

Example: x^2+x+1

Linear function: A quadratic function with n=1.

Example: x+1

Domain and Range:

Domain is the input set

Range is the output set

Let us define f: R-R given by f(x)=x

then, The domain is R and the Range is also R.

This function is also known as identity function.

Optimisation:

f(x) = x^2 

We optimise using derivatives.

f'(x) = 2x+2=0

f'' (x)= 2

We thus have a minimum as f'' >0

so, x=0

f(-1) = 2 which is the minimum value the function can take.