1. Definition of a derivative

  2. Rules for differentiation

  3. Optimization problems

Definition of a derivative

The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches 0:

fβ€²(a)=limhβ†’0[f(a+h)βˆ’f(a)]/hf'(a) = lim hβ†’0 [f(a+h) - f(a)] / h

Rules for differentiation

The several rules that allow us to differentiate functions more easily.

Optimization problems

Optimization problems involve finding the maximum or minimum value of a function subject to some constraints.

One common method for solving optimization problems is to use derivatives

There commonly associated with the general steps for solving an optimization problem:

  1. Read the problem carefully

  2. Identify the objective function

  3. Identify the constraints

  4. Find the derivative of the objective function

  5. Set the derivative equal to zero to find critical points

  6. Determine the nature of the critical points (maximum, minimum or neither)

  7. Check the endpoints of the feasible region (if any)

  8. Interpret the solution in the context of the problem

  9. Verify the solution

Last updated