1. Determine where f(c) is increasing. Find the local maximum and local minimum points: f(x) = 2.03 – 3.rº – 12.1 = 3. (10 Peints) f'(x) = 6x² – 6.0 – 12 = 6(x² – 3 – 2) = 6(x − 2)(x+1) >0 Increasing in (-00, - 1) U (2,-). Local Maximum: x = -1 Local Minimum: x = 2

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carsondayLv1

16 Feb 2023

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Keith LeannonLv2

24 Oct 2018

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4. (30 pts) EXPLANATION IS NOT REQUIRED, AND NO PARTIAL CREDIT WILL BE GIVEN. (I) The entire) graph of a function f is shown in the figure below. (a) Find the x-coordinates of all critical points of f (or write NONE). ANSWER : critical point (s) at x = (b) Find the x-coordinates of all local minima of f (or write NONE). ANSWER : local min (s) at x = (c) Find all values of x at which fattains its global minimum (or write NONE ANSWER : global min (s) at x = (d) Find the interval (or intervals) on which the derivative of fis increasing. ANSWER : derivative off is increasing on (II) The figure below shows the graphs of f, f', and f". Which curve is which? Fill in the blanks: A = -; B= 2; CD- 4. EXPLANATION IS NOT REQUIRED, AND NO PARTIAL CREDIT WILL BE GIVEN. (III) A function f' (derivative of f) is given f'(x) = (x - 2) e*. The following questions are about the function f. (a) Find all critical points of f (or write NONE). ANSWER : critical point (s) at x = (b) on what interval (or intervals) is f increasing ? ANSWER : f is increasing on (c) Find the point or points where f has a local maximum (or write NONE). ANSWER : local max at x = (d) Find the point or points where f has a local minimum. ANSWER: local min (s) at x = (e) Find f "(x), the second derivative of f. ANSWER : f''(x) = (f) Identify any inflection pionts. ANSWER : inflection point (s) at x = (g) Determine the intervals on which the function is concave up or concave down. ANSWER: fis CONCAVE UP on fis CONCAVE DOWN on

(i) If a function f is continuous for all x and if f has a local maximum at (-1,4) and a local minimum at (3,-2), which of the following statements must be true? (A) The graph of f has an inflection point somewhere between x = -1 and x = 3. (B) f'(-1) = 0. (C) The graph of f has a horizontal asymptote. (D) The graph of f has a horizontal tangent line at x = 3. (E) The graph of f intersects both axes. Answer:

2. Determine where f(x) is concave up: f(x) = x+ + 2r3 – 36.x2 + 4x + 5 (10 points) f'(x) = 4.x} + 6rº – 72x + 4 f"(x) = 12x² + 12. – 72 = 12(x² + - 6) = 12(x+3)(x - 2) > 0 Concave up in (- 00, -3) U (2,00)

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1. Determine where f(c) is increasing. Find the local maximum and local minimum points: f(x) = 2.03 – 3.rº – 12.1 = 3. (10 Peints) f'(x) = 6x² – 6.0 – 12 = 6(x² – 3 – 2) = 6(x − 2)(x+1) >0 Increasing in (-00, - 1) U (2,-). Local Maximum: x = -1 Local Minimum: x = 2

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