Monotonicity and Extrema of a Cubic

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Find increases, decreases and extrema.

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Avinash

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Monotonicity and Extrema of a Cubic


Monotonicity and Extrema of a CubicVersion en ligne Find increases, decreases and extrema. par Avinash 1 Let f(x) = x^3 - 6x^2 + 9x + 2. Find intervals where f(x) is increasing and decreasing. Identify local extrema using the first derivative test. a Increasing on (-∞, 1) and (3, ∞); decreasing on (1, 3). Local maximum at x = 1 with f(1) = 6; local minimum at x = 3 with f(3) = 2. b Increasing on (-∞, 2) and (2, ∞); decreasing on (2, 3). Local maximum at x = 2 with f(2) = 7; local minimum at x = 3 with f(3) =1. c Increasing on (-∞, 1) and (2, ∞); decreasing on (1, 2). Local maximum at x = 1 with f(1) = 6; local minimum at x = 2 with f(3) = 2. 2 Let f(x) = x^3 - 6x^2 + 9x + 2. Find the critical points. Choose one or more answers a 2,5 b 1,3 c 0,1 d -2,3 3 Let f(x) = x^3 - 6x^2 + 9x + 2. Find the increasing intervals. Choose one or more answers a (-∞, 1) and (3, ∞) b (∞, 1) and (3, -∞) c (-∞, 0) and (3, ∞) d (-∞, 1) and (1, ∞) 4 Let f(x) = x^3 - 6x^2 + 9x + 2. Find the decreasing intervals. Choose one or more answers a (-1,3) b (0,3) c (1, 3) d (-3,-1) 5 Let f(x) = x^3 - 6x^2 + 9x + 2. Find the local extreme values. Choose one or more answers a local minimum = (3,0) , local maximum = (1,4) b local minimum = (3,-2) , local maximum = (-1,6) c local minimum = (3,2) , local maximum = (1,6) d local minimum = (1,2) , local maximum = (1,5) 6 Let f(x) = x^3 - 6x^2 + 9x + 2. Find the points of inflection. Choose one or more answers a (0,2) b (2,4) c (1,3) d (0,4) 7 Let f(x) = x^3 - 6x^2 + 9x + 2. The interval for concave up will be Choose one or more answers a (-∞,2) b (3, ∞) c (2, ∞) d (0,2) 8 Let f(x) = x^3 - 6x^2 + 9x + 2. The interval for concave down will be Choose one or more answers a (-∞,2) b (3, ∞) c (2, ∞) d (0,2) 9 Let f(x) = x^3 - 6x^2 + 9x + 2. Find the second derivative at critical point x = 1 and 3 and also check local maxima or minima at these points. Choose one or more answers a f''(1) >0 Local Maximum: (1,6) and f''(3) <0 Local Minimum (3,2) b f''(1) =0 Local Maximum: (1,5) and f''(3) >0 Local Minimum (3,2) c f''(1) <0 Local Maximum: (1,6) and f''(3) =0 Local Minimum (3,3) d f''(1) <0 Local Maximum: (1,6) and f''(3) >0 Local Minimum (3,2)

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Monotonicity and Extrema of a Cubic

Test

À propos de cette activité

Créé par

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Monotonicity and Extrema of a CubicVersion en ligne

par Avinash

Let f(x) = x^3 - 6x^2 + 9x + 2. Find intervals where f(x) is increasing and decreasing. Identify local extrema using the first derivative test.

Let f(x) = x^3 - 6x^2 + 9x + 2. Find the critical points.

Choose one or more answers

Let f(x) = x^3 - 6x^2 + 9x + 2. Find the increasing intervals.

Choose one or more answers

Let f(x) = x^3 - 6x^2 + 9x + 2. Find the decreasing intervals.

Choose one or more answers

Let f(x) = x^3 - 6x^2 + 9x + 2. Find the local extreme values.

Choose one or more answers

Let f(x) = x^3 - 6x^2 + 9x + 2. Find the points of inflection.

Choose one or more answers

Let f(x) = x^3 - 6x^2 + 9x + 2. The interval for concave up will be

Choose one or more answers

Let f(x) = x^3 - 6x^2 + 9x + 2. The interval for concave down will be

Choose one or more answers

Let f(x) = x^3 - 6x^2 + 9x + 2. Find the second derivative at critical point x = 1 and 3 and also check local maxima or minima at these points.

Choose one or more answers