Q. 0 - Calculus

Question

Q.Read the section and make your own summary of the material.

Step-by-Step Solution

Answer

To find a global extremum of a continuous function we must compare the following:

• the values f(c) for each interior local extremum c ∈ I
• the values f(c) at any closed endpoints x = c of I
• the limits $\underset{x\to c}{lim}f\left(x\right)$ at any open endpoints or non-domain points x = c of I.

Many students have difficulty with word problems because of the translation step, not because of the mathematical solving step. This translating procedure is illustrated in the following diagram:

Step 1. Given Information.

The information in the book.

Step 2. Finding Global extrema.

To find a global extremum of a continuous function we must compare the following:

• the values f(c) for each interior local extremum c ∈ I
• the values f(c) at any closed endpoints x = c of I
• the limits $\underset{x\to c}{lim}f\left(x\right)$ at any open endpoints or non-domain points x = c of I.

Step 3. Translating Word Problems into Mathematical Problems.

Many students have difficulty with word problems because of the translation step, not because of the mathematical solving step. This translating procedure is illustrated in the following diagram: