Question

Let f(x) = 34x^4 - 53x^3 - x^2 + 2. Find (a) the domain of f, (b) the critical number(s), and (c) interval(s) where the function is increasing and decreasing. If there is more than one number or interval, separate answers with a semicolon. Type -INF for -âˆž and INF for âˆž. Responses must contain a simplified fraction, a/b, when necessary. Do not enter any spaces in your answers. You may use the quadratic formula where necessary. In part (c), use a sign chart, and do not use brackets in your answer. (a) The domain of f (in interval notation): (b) Critical number(s): x = (c) Interval(s) where the function is increasing: Interval(s) where the function is decreasing:

          Let f(x) = 34x^4 - 53x^3 - x^2 + 2. Find (a) the domain of f, (b) the critical number(s), and (c) interval(s) where the function is increasing and decreasing. If there is more than one number or interval, separate answers with a semicolon. Type -INF for -âˆž and INF for âˆž. Responses must contain a simplified fraction, a/b, when necessary. Do not enter any spaces in your answers. You may use the quadratic formula where necessary. In part (c), use a sign chart, and do not use brackets in your answer.

(a) The domain of f (in interval notation):
(b) Critical number(s): x =
(c) Interval(s) where the function is increasing:
Interval(s) where the function is decreasing:

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Calculus: Early Transcendentals

James Stewart 8th Edition

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Let f(x) = 34x^4 - 53x^3 - x^2 + 2. Find (a) the domain of f, (b) the critical number(s), and (c) interval(s) where the function is increasing and decreasing. If there is more than one number or interval, separate answers with a semicolon. Type -INF for -âˆž and INF for âˆž. Responses must contain a simplified fraction, a/b, when necessary. Do not enter any spaces in your answers. You may use the quadratic formula where necessary. In part (c), use a sign chart, and do not use brackets in your answer. (a) The domain of f (in interval notation): (b) Critical number(s): x = (c) Interval(s) where the function is increasing: Interval(s) where the function is decreasing:

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Transcript

00:01 So we're looking at the function defined as 12x cubed minus 99x squared minus 720x plus 6.

00:13 And we need to find the derivative of this.

00:15 It's just going to be our power rule.

00:18 Like 12 times 3 is 36.

00:20 You subtract 1 from the exponent.

00:23 99 times 2 is 198.

00:26 You subtract 1 from the exponent minus 720.

00:31 And the critical numbers will happen if that equals 0.

00:34 Now let's see if all these numbers are divisible by...

00:37 Maybe they're all divisible by 18.

00:40 See i think you can factor out an 18 there.

00:43 2x squared would be 11x when i divide.

00:47 And 720 divided by 18 is 40.

00:52 And i'm going to try and factor this.

00:54 So there's only one way of getting 2x squared.

00:56 That's 2x times x.

00:58 But then thinking about all the different ways you can get 40.

01:02 I'm just trying to ponder because it'd be like 80.

01:07 And let's see is 80 divisible by 4? but that's not going to work for me.

01:14 80 divisible by...

01:19 I want to say it's going to be 5 and 16.

01:27 And the only way to get the 16 is if you did 2 times 8.

01:32 And that's negative 16...

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