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AP Calculus Name ____________________________________ Analytic Applications of Differentiation Test #5-A Problems 1 –10, multiple choice. 2. What are all values of ݔ for which the function ݂ defined by ݂(ݔ) = (ݔଶ െ 3)݁ି௫ is increasing? A. ݔ > െ1 and ݔ < 3 B. െ1 < ݔ > 3 C. െ3 < ݔ > 1 D. All values of ݔ 1. Find all critical numbers for the function: ݂(ݔ) = (9 െ ݔଶ)ଷ/ହ A. {0} B. {െ3, 3} C. {3} D. {െ3, 0, 3} 3. Let ݄(ݔ (be a twice-differentiable function with ݄ᇱ (ݔ > (0 and ݄ᇱᇱ(ݔ > (0 for all real numbers ݔ, such that ݄(2) = 14 and ݄(3) = 5. Of the following, which is a possible value for ݄(4) ? A. 10 B. 4 C. െ5 D. 1 Calculator is NOT ALLOWED on this test! This study source was downloaded by 100000874405579 from CourseHero.com on 11-30-2023 01:42:31 GMT -06:00 https://www.coursehero.com/file/77883988/Copy-of-Unit-5-Assessmentpdf/ © Jean Adams Flamingo MathTM, LLC 4. The graph of ݂ᇱ (ݔ(, the derivative of a function ݂(ݔ(, is shown at right. Which of the following statements is/are true? A. The graph of ݂ has a point of inflection at ݔ = ܽ B. ݂ is not continuous at ݔ = ܽ C. ݂ has a relative maximum at ݔ = ܽ D. ݂ is continuous but not differentiable at ݔ = ܽ 5. Find the values of ݔ where the graph of the function has a point of inflection. Given: ݂(ݔ = (ݔସ െ ݔଷ ଵ = ݔ 0, = ݔ .B 0 = ݔ .A ଶ ଷ = ݔ , 0 = ݔ .C ସ D. ݔ = ଵ ଶ 6. The graph of the second derivative of a function ݂(ݔ (is shown at right. Which of the following is/are true? I. The graph of ݂(ݔ (has a point of inflection at ݔ – = 1. II. The graph of ݂(ݔ (is concave down on the interval (– 1, 3). III. The graph ݂ Ԣ (ݔ (is decreasing at ݔ = 2. A. I only B. II only C. I and II onl