Cusp Points and the Derivative (8.4.2)

Question 1

• Functions with fractional exponents could potentially have cusp points. A cusp point is a point where the curve abruptly changes direction.

Answer 1

• Functions with fractional exponents could potentially have cusp points. A cusp point is a point where the curve abruptly changes direction.

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.