FIRST AND SECOND DERIVATIVE TEST AND GRAPHING C

1. Given f(x) = x³ - 12 x + 5 • Find all of

2. Given f’’(x) = x(x²-4), where is f(x) concave up? • A) (-∞, 0)

3. For what values of x does the graph f(x) = x⁴ - 4

4. The function f(x) has a first derivative given by f’(x) = x(x –

6. Given f(x) = 5 + 3 x² - x³ • Sketch a graph

Answers • #1 Incr (-∞, -2) and (2, ∞) Decr (-2, 2) Max (-2,

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FIRST AND SECOND DERIVATIVE TEST AND GRAPHING C C. 4 – C. 7 Review

1. Given f(x) = x³ - 12 x + 5 • Find all of the following: • Intervals on which it is increasing • Intervals on which it is decreasing • Any extrema • Intervals on which it is concave up • Intervals on which it is concave down • Any inflection points

2. Given f’’(x) = x(x²-4), where is f(x) concave up? • A) (-∞, 0) • B) (-2, 0) and (2, ∞) • C) (-∞ -2) and (2, ∞) • D) (2, 0)

3. For what values of x does the graph f(x) = x⁴ - 4 x³ + 2 have a point of inflection? • A) x = -1 ONLY • B) x = 0 ONLY • C) x = -2, 0 and 2 • D) x = 0 and 2 • E) x = 2 ONLY

4. The function f(x) has a first derivative given by f’(x) = x(x – 5)²(x + 3). Where does f(x) have a relative minimum? • A) x = 5 ONLY • B) x = 0 ONLY • C) x = -3, 0, and 5 • D) x = 0 and 5 • E) x = -3 and 5

6. Given f(x) = 5 + 3 x² - x³ • Sketch a graph the function using the tests you know! • X int (set equation = 0): Y int (set x = 0): • • Increasing: Decreasing: Extrema: Concave Down: Point of • • • Concave Up: Inflection:

Answers • #1 Incr (-∞, -2) and (2, ∞) Decr (-2, 2) Max (-2, 21) Min (2, -11) • CU (0, ∞) CD (-∞, 0) POI (0, 5) • #2 B • #3 D • #4 B • #5 A • #6 ->