Overview
- Definition of a derivative
- Rules for differentiation
- 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:
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.
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There commonly associated with the general steps for solving an optimization problem:
- Read the problem carefully
- Identify the objective function
- Identify the constraints
- Find the derivative of the objective function
- Set the derivative equal to zero to find critical points
- Determine the nature of the critical points (maximum, minimum or neither)
- Check the endpoints of the feasible region (if any)
- Interpret the solution in the context of the problem
- Verify the solution