1οΈDerivatives
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.
One common method for solving optimization problems is to use derivatives
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
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