Domain-Restricted Functions and the Derivative (8.4.3)

Question 1

• If the variable of a function is raised to a fractional exponent that has an even denominator, the function may not be defined for all real numbers.

Answer 1

• If the variable of a function is raised to a fractional exponent that has an even denominator, the function may not be defined for all real numbers.

Question 2

• To graph a function:

1. Find critical points using the first derivative.
2. Determine where the function is increasing or decreasing.
3. Find inflection points using the second derivative.
4. Determine where the function is concave up or concave down

Answer 2

• To graph a function:

1. Find critical points using the first derivative.
2. Determine where the function is increasing or decreasing.
3. Find inflection points using the second derivative.
4. Determine where the function is concave up or concave down

Question 3

• On an interval, the sign of the first derivative indicates whether the function is increasing or decreasing. The sign of the second derivative indicates whether the function is concave up or concave down.

Answer 3

• On an interval, the sign of the first derivative indicates whether the function is increasing or decreasing. The sign of the second derivative indicates whether the function is concave up or concave down.