Lesson 13: Analyzing Other Types of Functions

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Presentation transcript:

Lesson 13: Analyzing Other Types of Functions math 1314 Lesson 13: Analyzing Other Types of Functions

Critical Numbers versus Critical Points

Geogebra Command Reminders:

Popper 14: The graph illustrated is f’(x), the first derivative of some function f(x). f(x) is defined on (-∞, 0)  (0, ∞). Determine the critical values for f(x). a. 0 b. -0.5 c. 0.5 d. 3 e. All of these 2. Where is one interval that f(x) is increasing? a. (-∞,-0.5) b. (0.5, 3) c. (0, 0.5) d. (0.5, ∞) 3. Determine the location of relative maximum: a. x = -0.5 b. x = 0 c. x = 0.5 d. x = 3 e. No Rel Max 4. Where is one interval where f”(x) is positive? a. (0, 3) b. (- ∞, 0) c. (3, ∞) d. (0, 0.5) 5. Where is one interval where f(x) is concave down? a. (0, 3) b. (- ∞, 0) c. (3, ∞) d. (0, 3) 6. Determine the location of a point of inflection. a. x = 3 b. x = 0 c. x = 0.5 d. No points of inflection

Continued on Next Slide

Popper 15: Consider the following function: 𝑓 𝑥 = 𝑥∙ 3 𝑥−5 𝑥+4 Determine the domain of f(x): [5,∞) b. (-∞,-4)(-4,∞) c. (-4,∞) d. (-∞, ∞) 2. Determine the critical numbers of f(x): -4, 5 b. -4, 3.1355, 8.1221 c. -4, 3.1355, 5 d. 8.1221 3. Where is f(x) increasing: (3.1335, 5) b. (0, ∞) c. (0,5) d. (3.1335, ∞)

Popper 15: 4. Determine the location of a relative maximum: a. 3.1335 b. -4 c. 5 d. No Relative Minimum 5. Where is f(x) concave up? (-∞, -4) b. (-4, 5) c. (5, ∞) d. Never 6. Where is the location of an inflection point? a. x = -4 b. x = 5 c. x = -4 & 5 d. No Inflection Points